CFD Benchmark - User contributions [en]

Performances

2020-10-01T14:44:27Z

Abdelsamie:

The results presented above were obtained on different architectures, preventing the direct comparison of the performance of the codes.
However, the TauBench pseudo-benchmark~\cite{TauBench,TauBench2} made it possible to assess in a separate test the raw performance of each machine.
The following sections will describe the configuration of the three high performance
computing (HPC) systems that were used to run YALES2, DINO and Nek5000 for the TGV benchmarks.
Subsequently, the TauBench methodology and its results on the target computers will be presented.
Finally, the performance analysis for the 3-D TGV cases is discussed in the last subsection.

= Presentation of the machines used for the benchmark =

== Irene Joliot-Curie from TGCC ==

The YALES2 results were obtained on the Irene Joliot-Curie machine~\cite{irene} operated by TGCC/CEA for GENCI (French National Agency for Supercomputing).
%This machine built by Atos was introduced in Sept. 2018 and is ranked at the 61th position of June 2020 Top500 ranking~\cite{ireneTop500}.
It is composed of 1,656 compute nodes, with 192 GB memory on each node and two sockets of Intel Skylake (Xeon Platinum 8168) with 24 cores each, operating at 2.7 GHz.
Each core can deliver a theoretical peak performance of 86.4 GFlop/s with AVX-512 and FMA activated.
The interconnect is an Infiniband EDR, and the theoretical maximum bandwidth is 128 GB/s per socket and thus 5.33 GB/s by core when all cores are active.
The software stack consists of the Intel Compiler 19 and OpenMPI 2.0.4, both used for all results obtained in this benchmark.

== SuperMUC-NG from LRZ ==

All test cases with DINO were simulated on the SuperMUC machine, hosted at the Leibniz Supercomputing Center (LRZ) in Munich, Germany~\cite{supermuc}.
In the course of the project, results have been obtained on three versions of SuperMUC (Phase I, Phase II, and NG), but
only the performance on the most recent system, SuperMUC-NG, will be discussed here.
%This machine was assembled by Lenovo and ranks at the 13th position at June 2020 Top500~\cite{supermucTop500}.
SuperMUC-NG is a combination of 6,336 compute nodes built from bi-socket Intel Skylake Xeon Platinum Processor 8174 with 96 GB of memory and 24 cores.
The theoretical peak performance of a single core is 99.2 GFlop/s with AVX512 and FMA activated at a sustained frequency of 3.1 GHz.
The nodes are interconnected with Intel OmniPath interconnect network. All tests presented here were obtained with the Intel 19 compiler and Intel MPI.

== Piz Daint from CSCS ==

The Nek5000 simulations were performed on the XC40 partition of the Piz Daint machine at CSCS in Switzerland~\cite{pizdaint}.
%This machine ranks at the 231th position of the June 2020 Top500 ranking~\cite{pizdaintTop500} and was manufactured by HPE and Cray.
It is composed of 1,813 compute nodes, each containing 64~GB of RAM and two sockets using the Intel Xeon E5-2695~v4 processors (18 cores at 2.1 GHz by socket).
The theoretical peak performance of a single core is 33.6~GFlop/s with AVX2 and FMA activated.
The interconnect is based on the Aries routing and communications ASIC and a Dragonfly
network topology, and the maximum achievable bandwidth (BW) with a single socket is 76.8 GB/s,
which allows 4.27~GB/s transfer to each core in a fully occupied socket.
All tests presented here have been obtained with the Intel 18 compiler.

= TauBench performance benchmark =

The scalable benchmark TauBench emulates the run time behavior of the compressible TAU flow solver~\cite{dlr22421} with respect to the memory footprint and floating-point performance.
Since the TAU solver relies on unstructured grids, its most important property is that all access points to the grid are indirect, as in most modern CFD solvers.
TauBench can therefore be used to estimate the performance of a generic flow solver with respect to machine properties, like memory bandwidth or cache miss/latencies.
It is used to provide a reference measurement of a system on a workload that is more representative of usual CFD codes than the widely used LINPACK benchmark~\cite{linpack}, which is mostly CPU-bound.
Even though some important effects are neglected by using a single-core benchmark (like MPI communications or memory bandwidth saturation that appear on fully-filled nodes), TauBench is still a good indicator of the relative performance of each architecture.

{| class="wikitable alternance center"
|+ Single-core performance obtained by TauBench for the three HPC systems employed in the benchmarks
|-
! scope="col" | Machine
! scope="col" | Irene Joliot-Curie
! scope="col" | SuperMuc-NG
! scope="col" | Pitz Daint
|-
! scope="row" | Frequency [GHz]
| 2.7
| 3.1
| 2.1
|-
! scope="row" | Single core TauBench [GFlop/s]
| 2.97
| 3.34
| 4.13
|-
! scope="row" | Single core Peak [GFlop/s]
| 86.4
| 99.2
| 33.6
|-
! scope="row" | Single core BW [GB/s]
| 21.3
| 21.3
| 19.2
|}

This table presents some important data of the three considered HPC systems: the processor frequency, the result ofTauBench, the theoretical peak performance and the memory bandwidth. The last three results are given for a singlecore. The most striking – though not unexpected – conclusion is that TauBench provides results that are much lowerthan the theoretical peak performance (3% of the peak for Irene Joliot-Curie and for SuperMUC-NG, and 12% forPitz Daint). This is in agreement with the results from the similar and well-known benchmark HPCG [86] that is alsointended as a complement to the High Performance LINPACK (HPL) benchmark, currently used to rank the Top500computing systems. For example, the HPCG benchmark on the Irene Joliot-Curie revealed a peak performanceof 0.66 GFlop/s per core [87], which is approximately only 0.8% of the peak performance. The main reason forthe discrepancy between the LINPACK and the HPCG benchmark is that the first one is purely CPU-bound whileHPCG is mostly limited by the memory bandwidth and cache-miss effects. TauBench is somewhere in between andis probably a good estimate for many CFD codes.Indeed, the theoretical peak performance can only be reached when performing 2 fully-vectorized Fused Multiply-Add (FMA) instructions per cycle. This situation is never achieved in any CFD code. Most of them are usuallylimited to issuing only one non-vectorized non-FMA instruction per cycle; in this situation, the peak performance (inGFlop/s) is simply equal to the processor frequency (in GHz). This can be observed very clearly on SuperMUC andIrene Joliot-Curie. Regarding the Pitz Daint machine, it appears that the TauBench result is actually much betterthere than on the two other machines when compared to theoretical peak performance; this is somewhat unexpectedand might be due to the use of TurboBoost on this machine, or to a better memory/cache performance.It should be pointed out that no effort was made to find the best parameters (tolerances, timestep, etc.) tominimize the computational cost, and the following results should only be considered as indicative of the time-to-solution of the three codes.

= Methodology =
Several metrics will be used in the following sections to characterize the codes. They are introduced by givingboth a formal definition as well as a few complementary explanations. In order to avoid any confusion between CPUtime and Simulated time, the corresponding data will be indexed by <sub>CPU</sub> and <sub>Sim</sub>, respectively.

First, the Wall-Clock Time (WCT) is the elapsed time to perform a simulation on a given number of cores Ncores.The product TCPU = Ncores×WCT is thus the total CPU time for the simulation.A more meaningful metric is the so-called Reduced Computational Time (RCT), which is computed as:

<math>
RTC = \frac{TCPU}{Nit \times N_p}
</math>

Analysis of Step 1

2020-10-01T14:39:40Z

Abdelsamie:

The verification involves a direct comparison with the analytical solution. For this purpose, analytic fields for
'''velocity''' (x- and y-components) and '''vorticity''' <math>(\partial_x v - \partial_y u)</math> at <math>t=10 \tau_{ref}</math> are presented in Fig. 3. It should be noted
that both '''YALES2''' and '''DINO''' used 642 '''grid points''' for this test case, while '''Nek5000''' employed 82
'''spectral elements of order 8''', which results in 64 '''discretization points''' in each direction. The velocity profiles along both centerlines of
the domain at <math>t = 10 \tau_{ref}</math> are shown in Fig. 4. It can be observed that the three codes give perfect visual agreement
14
with the '''analytical solution'''. Table 3 present the analytical maximal velocity at <math>t = 10 \tau_{ref}</math> (as computed from Eq. 2)
and the values obtained with the three codes, as well as the associated relative error: it is observed that the maximal
deviation is less than <math>0.03%</math> for the three codes.

{| class="wikitable alternance center"
|+ Comparison of the peak velocity at <math>t = 10 \tau_{ref}</math> for Step 1 (verification)
|-
|
! scope="col" | Analytical
! scope="col" | YALES2
! scope="col" | DINO
! scope="col" | Nek5000
|-
! scope="row" | <math>V_{max}</math>
| 0.9875778
| 0.987583
| 0.987565
| 0.9875785
|-
! scope="row" | <math>\epsilon_{rel}</math>
| 0 [Ref]
| <math>5.3·10^{-4}%</math>
| <math>1.3·10^{-3}%</math>
| <math>7.1·10^{-5}%</math>
|}

This configuration, although quite far from any realistic flame, is nevertheless an excellent manner to verify the
numerical procedure. It can be used to check the obtained discretization order in space and time and to quantify
numerical dissipation, as documented for instance in Figure 5 of <ref name="abelsamie2016"/>.

[[File:vx_t2.png|250px|alt text]]
[[File:vy_t2.png|250px|alt text]]
[[File:wz_t2.png|250px|alt text]]

You can see on the figures above the analytic fields of x-velocity, y-velocity, and vorticity, respectively (from left to right), at <math>t = 10 \tau_{ref}</math> for '''Step 1''' (verification step).

[[File:vx_2d.png|250px]]
[[File:vy_2d.png|250px]]

Comparing the results of the '''three codes''' with the analytical solution for the '''2-D Taylor-Green vortex''' ('''Step 1'''). Left: xcomponent of velocity. Right: y-component of velocity.

= References =

<references>
<ref name="abelsamie2016">
<bibtex>
@article{Abdelsamie2016,
author= {A. Abdelsamie and G. Fru and F. Dietzsch and G. Janiga and D. Thévenin},
title= {Towards direct numerical simulations of low-Mach number turbulent reacting and two-phase flows using immersed boundaries},
journal={Comput. Fluids},
year= {2016},
volume={131},
number={5},
pages={123--141},
}
</bibtex>
</ref>
</references>

Performances

2020-10-01T14:33:21Z

Abdelsamie: /* TauBench performance benchmark */

Performances

2020-10-01T14:32:21Z

Abdelsamie:

Performances

2020-09-26T21:11:44Z

Abdelsamie:

Performances

2020-09-26T21:07:36Z

Abdelsamie:

Performances

2020-09-26T18:09:21Z

Abdelsamie:

Performances

2020-09-26T18:07:32Z

Abdelsamie: /* Irene Joliot-Curie from TGCC */

Performances

2020-09-26T18:05:14Z

Abdelsamie:

Performances

2020-09-26T18:02:37Z

Abdelsamie: Created page with "The results presented above were obtained on different architectures, preventing the direct comparison of the performance of the codes. However, the TauBench pseudo-benchmark~..."

File:Step13b dino space.txt

2020-09-24T00:14:57Z

Abdelsamie: Abdelsamie uploaded a new version of File:Step13b dino space.txt

Results of Step 3 with DINO.

This file contains 7 columns:

the position on the x-axis [cm]

the x-component of the velocity [m/s]

the position on the y-axis [cm]

the y-component of the velocity [m/s]

the temperature [K]

the mass fraction of H2 [-]

the mass fraction of O2 [-]

File:YOH nek5000.txt

2020-09-21T21:50:56Z

Abdelsamie:

File:YOH 514.txt

2020-09-21T21:50:34Z

Abdelsamie:

File:YOH 253.txt

2020-09-21T21:50:07Z

Abdelsamie:

File:YO2 514.txt

2020-09-21T21:49:33Z

Abdelsamie: Abdelsamie uploaded a new version of File:YO2 514.txt

File:YO2 nek5000.txt

2020-09-21T21:26:16Z

Abdelsamie:

File:YO2 514.txt

2020-09-21T21:25:43Z

Abdelsamie:

File:YO2 253.txt

2020-09-21T21:22:27Z

Abdelsamie:

File:YH2 nek5000.txt

2020-09-21T21:18:28Z

Abdelsamie:

File:YH2 514.txt

2020-09-21T21:17:53Z

Abdelsamie:

File:YH2 253.txt

2020-09-21T21:17:21Z

Abdelsamie:

File:Vy nek5000.txt

2020-09-21T21:15:42Z

Abdelsamie:

File:Vy 514.txt

2020-09-21T21:14:59Z

Abdelsamie:

File:Vy 253.txt

2020-09-21T21:13:05Z

Abdelsamie:

File:Vx nek5000.txt

2020-09-21T21:09:18Z

Abdelsamie:

File:Vx 514.txt

2020-09-21T21:08:32Z

Abdelsamie:

File:Vx 253.txt

2020-09-21T21:07:41Z

Abdelsamie:

File:T nek5000.txt

2020-09-21T21:06:26Z

Abdelsamie:

File:T 514.txt

2020-09-21T21:05:52Z

Abdelsamie:

Results

2020-09-21T21:05:08Z

Abdelsamie: /* Step 4 */

The results of the Benchmark are organized as follows:

= Yales2 =

== Step 1 ==

This is a link to get the file [[File:Step11b_Ux_vs_x_10.0s_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step11b_Uy_vs_y_10.0s_CORIA_YALES2.txt]].

== Step 2 ==

This is a link to get the file [[File:Step2 YALES2 512 CFL0.10.txt]].

This is a link to get the file [[File:Step2 YALES2 512 CFL0.20.txt]].

This is a link to get the file [[File:Step2 YALES2 512 CFL0.30.txt]].

This is a link to get the file [[File:Step2 YALES2 512 CFL0.60.txt]].

This is a link to get the file [[File:Step12a_description_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step12b_12.11s_Ux_vs_x_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step12b_12.11s_Uy_vs_y_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step12b_12.11s_Wz_vs_x_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step12b_EPS_vs_t_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step12b_KE_vs_t_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step12c_scaling_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step12d_PressureConvergence_CORIA_YALES2.txt]].

== Step 3 ==

This is a link to get the file [[File:Step13a_description_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step13b_0.0ms_T_vs_x_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step13b_0.0ms_YH2_vs_x_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step13b_0.0ms_YO2_vs_x_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step13b_0.5ms_T_vs_y_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step13b_0.5ms_Ux_vs_x_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step13b_0.5ms_Uy_vs_y_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step13b_0.5ms_YH2_vs_y_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step13b_0.5ms_YO2_vs_y_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step13c_CORIA_YALES2.txt]].

== Step 4 ==

=== <math>256^3</math> ===

This is a link to get the file [[File:Step2b_0.0ms_T_vs_x_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step2b_0.0ms_YH2_vs_x_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step2b_0.0ms_YO2_vs_x_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step2b_0.5ms_HRR_vs_y_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step2b_0.5ms_T_vs_y_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step2b_0.5ms_Ux_vs_x_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step2b_0.5ms_Uy_vs_y_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step2b_0.5ms_YH2_vs_y_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step2b_0.5ms_YO2_vs_y_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step2b_0.5ms_YOH_vs_y_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step2b_P_vs_t_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step2b_Tmax_vs_t_CORIA_YALES2.txt]].

=== <math>384^3</math> ===

This is a link to get the file [[File:Step2b_0.0ms_T_vs_x_CORIA_YALES2_384.txt]].

This is a link to get the file [[File:Step2b_0.0ms_YH2_vs_x_CORIA_YALES2_384.txt]].

This is a link to get the file [[File:Step2b_0.0ms_YO2_vs_x_CORIA_YALES2_384.txt]].

This is a link to get the file [[File:Step2b_0.5ms_HRR_vs_y_CORIA_YALES2_384.txt]].

This is a link to get the file [[File:Step2b_0.5ms_T_vs_y_CORIA_YALES2_384.txt]].

This is a link to get the file [[File:Step2b_0.5ms_Ux_vs_x_CORIA_YALES2_384.txt]].

This is a link to get the file [[File:Step2b_0.5ms_Uy_vs_y_CORIA_YALES2_384.txt]].

This is a link to get the file [[File:Step2b_0.5ms_YH2_vs_y_CORIA_YALES2_384.txt]].

This is a link to get the file [[File:Step2b_0.5ms_YO2_vs_y_CORIA_YALES2_384.txt]].

This is a link to get the file [[File:Step2b_0.5ms_YOH_vs_y_CORIA_YALES2_384.txt]].

This is a link to get the file [[File:Step2b_P_vs_t_CORIA_YALES2_384.txt]].

This is a link to get the file [[File:Step2b_Tmax_vs_t_CORIA_YALES2_384.txt]].

=== <math>512^3</math> ===

This is a link to get the file [[File:Step2b_0.0ms_T_vs_x_CORIA_YALES2_512.txt]].

This is a link to get the file [[File:Step2b_0.0ms_YH2_vs_x_CORIA_YALES2_512.txt]].

This is a link to get the file [[File:Step2b_0.0ms_YO2_vs_x_CORIA_YALES2_512.txt]].

This is a link to get the file [[File:Step2b_0.5ms_HRR_vs_y_CORIA_YALES2_512.txt]].

This is a link to get the file [[File:Step2b_0.5ms_T_vs_y_CORIA_YALES2_512.txt]].

This is a link to get the file [[File:Step2b_0.5ms_Ux_vs_x_CORIA_YALES2_512.txt]].

This is a link to get the file [[File:Step2b_0.5ms_Uy_vs_y_CORIA_YALES2_512.txt]].

This is a link to get the file [[File:Step2b_0.5ms_YH2_vs_y_CORIA_YALES2_512.txt]].

This is a link to get the file [[File:Step2b_0.5ms_YO2_vs_y_CORIA_YALES2_512.txt]].

This is a link to get the file [[File:Step2b_0.5ms_YOH_vs_y_CORIA_YALES2_512.txt]].

This is a link to get the file [[File:Step2b_P_vs_t_CORIA_YALES2_512.txt]].

This is a link to get the file [[File:Step2b_Tmax_vs_t_CORIA_YALES2_512.txt]].

= Nek5000 =

== Step 1 ==

This is a link to get the file [[File:NEK500_Step1_Ux_vs_x_t10.txt]].

This is a link to get the file [[File:NEK500_Step1_Uy_vs_y_t10.txt]].

== Step 2 ==

This is a link to get the file [[File:Step12a_ETH.txt]].

This is a link to get the file [[File:Step12b_ETH_t9.33864.txt]].

This is a link to get the file [[File:Step12b_ETH_t12.11.txt]].

This is a link to get the file [[File:Step12b_ETH_t12.11_space.txt]].

This is a link to get the file [[File:Step12b_ETH_t12.11_time.txt]].

This is a link to get the file [[File:Step12c_ETH.txt]].

== Step 3 ==

This is a link to get the file [[File:Step13a_ETH.txt]].

This is a link to get the file [[File:Step13b_ETH.txt]].

This is a link to get the file [[File:Step13b_ETH_space.txt]].

This is a link to get the file [[File:Step13b_ETH_time.txt]].

This is a link to get the file [[File:Step13c_ETH.txt]].

== Step 4 ==

This is a link to get the file [[File:HRR_253.txt]].

This is a link to get the file [[File:HRR_514.txt]].

This is a link to get the file [[File:HRR_nek5000.txt]].

This is a link to get the file [[File:profs.txt]].

This is a link to get the file [[File:T.txt]].

This is a link to get the file [[File:T_253.txt]].

This is a link to get the file [[File:T_514.txt]].

This is a link to get the file [[File:T_nek5000.txt]].

This is a link to get the file [[File:Vx_253.txt]].

This is a link to get the file [[File:Vx_514.txt]].

This is a link to get the file [[File:Vx_nek5000.txt]].

This is a link to get the file [[File:Vy_253.txt]].

This is a link to get the file [[File:Vy_514.txt]].

This is a link to get the file [[File:Vy_nek5000.txt]].

This is a link to get the file [[File:YH2_253.txt]].

This is a link to get the file [[File:YH2_514.txt]].

This is a link to get the file [[File:YH2_nek5000.txt]].

This is a link to get the file [[File:YO2_253.txt]].

This is a link to get the file [[File:YO2_514.txt]].

This is a link to get the file [[File:YO2_nek5000.txt]].

This is a link to get the file [[File:YOH_253.txt]].

This is a link to get the file [[File:YOH_514.txt]].

This is a link to get the file [[File:YOH_nek5000.txt]].

= DINO =

== Step 1 ==

This is a link to get the file [[File:DINO_Step11b_dino.txt]].

== Step 2 ==

This is a link to get the file [[File:epsVStime.txt]].

This is a link to get the file [[File:kVStime.txt]].

This is a link to get the file [[File:Step2b_dino_space.txt]].

== Step 3 ==

This is a link to get the file [[File:Step13b_dino_time.txt]].

This is a link to get the file [[File:Step13b_dino_space.txt]].

== Step 4 ==

This is a link to get the file [[File:Step2b_dino_space_384.txt]].

This is a link to get the file [[File:Step2b_dino_space_512.txt]].

This is a link to get the file [[File:Step2b_dino_space_768.txt]].

This is a link to get the file [[File:Step2b_dino_time.txt]].

This is a link to get the file [[File:Step2b_dino_time_256.txt]].

This is a link to get the file [[File:Step2b_dino_time_384.txt]].

File:T 253.txt

2020-09-21T21:04:33Z

Abdelsamie:

Results

2020-09-21T21:02:28Z

Abdelsamie: /* Step 4 */

The results of the Benchmark are organized as follows:

= Yales2 =

== Step 1 ==

This is a link to get the file [[File:Step11b_Ux_vs_x_10.0s_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step11b_Uy_vs_y_10.0s_CORIA_YALES2.txt]].

== Step 2 ==

This is a link to get the file [[File:Step2 YALES2 512 CFL0.10.txt]].

This is a link to get the file [[File:Step2 YALES2 512 CFL0.20.txt]].

This is a link to get the file [[File:Step2 YALES2 512 CFL0.30.txt]].

This is a link to get the file [[File:Step2 YALES2 512 CFL0.60.txt]].

This is a link to get the file [[File:Step12a_description_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step12b_12.11s_Ux_vs_x_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step12b_12.11s_Uy_vs_y_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step12b_12.11s_Wz_vs_x_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step12b_EPS_vs_t_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step12b_KE_vs_t_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step12c_scaling_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step12d_PressureConvergence_CORIA_YALES2.txt]].

== Step 3 ==

This is a link to get the file [[File:Step13a_description_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step13b_0.0ms_T_vs_x_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step13b_0.0ms_YH2_vs_x_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step13b_0.0ms_YO2_vs_x_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step13b_0.5ms_T_vs_y_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step13b_0.5ms_Ux_vs_x_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step13b_0.5ms_Uy_vs_y_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step13b_0.5ms_YH2_vs_y_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step13b_0.5ms_YO2_vs_y_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step13c_CORIA_YALES2.txt]].

== Step 4 ==

=== <math>256^3</math> ===

This is a link to get the file [[File:Step2b_0.0ms_T_vs_x_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step2b_0.0ms_YH2_vs_x_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step2b_0.0ms_YO2_vs_x_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step2b_0.5ms_HRR_vs_y_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step2b_0.5ms_T_vs_y_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step2b_0.5ms_Ux_vs_x_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step2b_0.5ms_Uy_vs_y_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step2b_0.5ms_YH2_vs_y_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step2b_0.5ms_YO2_vs_y_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step2b_0.5ms_YOH_vs_y_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step2b_P_vs_t_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step2b_Tmax_vs_t_CORIA_YALES2.txt]].

=== <math>384^3</math> ===

This is a link to get the file [[File:Step2b_0.0ms_T_vs_x_CORIA_YALES2_384.txt]].

This is a link to get the file [[File:Step2b_0.0ms_YH2_vs_x_CORIA_YALES2_384.txt]].

This is a link to get the file [[File:Step2b_0.0ms_YO2_vs_x_CORIA_YALES2_384.txt]].

This is a link to get the file [[File:Step2b_0.5ms_HRR_vs_y_CORIA_YALES2_384.txt]].

This is a link to get the file [[File:Step2b_0.5ms_T_vs_y_CORIA_YALES2_384.txt]].

This is a link to get the file [[File:Step2b_0.5ms_Ux_vs_x_CORIA_YALES2_384.txt]].

This is a link to get the file [[File:Step2b_0.5ms_Uy_vs_y_CORIA_YALES2_384.txt]].

This is a link to get the file [[File:Step2b_0.5ms_YH2_vs_y_CORIA_YALES2_384.txt]].

This is a link to get the file [[File:Step2b_0.5ms_YO2_vs_y_CORIA_YALES2_384.txt]].

This is a link to get the file [[File:Step2b_0.5ms_YOH_vs_y_CORIA_YALES2_384.txt]].

This is a link to get the file [[File:Step2b_P_vs_t_CORIA_YALES2_384.txt]].

This is a link to get the file [[File:Step2b_Tmax_vs_t_CORIA_YALES2_384.txt]].

=== <math>512^3</math> ===

This is a link to get the file [[File:Step2b_0.0ms_T_vs_x_CORIA_YALES2_512.txt]].

This is a link to get the file [[File:Step2b_0.0ms_YH2_vs_x_CORIA_YALES2_512.txt]].

This is a link to get the file [[File:Step2b_0.0ms_YO2_vs_x_CORIA_YALES2_512.txt]].

This is a link to get the file [[File:Step2b_0.5ms_HRR_vs_y_CORIA_YALES2_512.txt]].

This is a link to get the file [[File:Step2b_0.5ms_T_vs_y_CORIA_YALES2_512.txt]].

This is a link to get the file [[File:Step2b_0.5ms_Ux_vs_x_CORIA_YALES2_512.txt]].

This is a link to get the file [[File:Step2b_0.5ms_Uy_vs_y_CORIA_YALES2_512.txt]].

This is a link to get the file [[File:Step2b_0.5ms_YH2_vs_y_CORIA_YALES2_512.txt]].

This is a link to get the file [[File:Step2b_0.5ms_YO2_vs_y_CORIA_YALES2_512.txt]].

This is a link to get the file [[File:Step2b_0.5ms_YOH_vs_y_CORIA_YALES2_512.txt]].

This is a link to get the file [[File:Step2b_P_vs_t_CORIA_YALES2_512.txt]].

This is a link to get the file [[File:Step2b_Tmax_vs_t_CORIA_YALES2_512.txt]].

= Nek5000 =

== Step 1 ==

This is a link to get the file [[File:NEK500_Step1_Ux_vs_x_t10.txt]].

This is a link to get the file [[File:NEK500_Step1_Uy_vs_y_t10.txt]].

== Step 2 ==

This is a link to get the file [[File:Step12a_ETH.txt]].

This is a link to get the file [[File:Step12b_ETH_t9.33864.txt]].

This is a link to get the file [[File:Step12b_ETH_t12.11.txt]].

This is a link to get the file [[File:Step12b_ETH_t12.11_space.txt]].

This is a link to get the file [[File:Step12b_ETH_t12.11_time.txt]].

This is a link to get the file [[File:Step12c_ETH.txt]].

== Step 3 ==

This is a link to get the file [[File:Step13a_ETH.txt]].

This is a link to get the file [[File:Step13b_ETH.txt]].

This is a link to get the file [[File:Step13b_ETH_space.txt]].

This is a link to get the file [[File:Step13b_ETH_time.txt]].

This is a link to get the file [[File:Step13c_ETH.txt]].

== Step 4 ==

This is a link to get the file [[File:HRR_253.txt]].

This is a link to get the file [[File:HRR_514.txt]].

This is a link to get the file [[File:HRR_nek5000.txt]].

This is a link to get the file [[File:profs.txt]].

This is a link to get the file [[File:T.txt]].

This is a link to get the file [[File:T_253:.txt]].

This is a link to get the file [[File:T_514.txt]].

This is a link to get the file [[File:T_nek5000.txt]].

This is a link to get the file [[File:Vx_253.txt]].

This is a link to get the file [[File:Vx_514.txt]].

This is a link to get the file [[File:Vx_nek5000.txt]].

This is a link to get the file [[File:Vy_253.txt]].

This is a link to get the file [[File:Vy_514.txt]].

This is a link to get the file [[File:Vy_nek5000.txt]].

This is a link to get the file [[File:YH2_253.txt]].

This is a link to get the file [[File:YH2_514.txt]].

This is a link to get the file [[File:YH2_nek5000.txt]].

This is a link to get the file [[File:YO2_253.txt]].

This is a link to get the file [[File:YO2_514.txt]].

This is a link to get the file [[File:YO2_nek5000.txt]].

This is a link to get the file [[File:YOH_253.txt]].

This is a link to get the file [[File:YOH_514.txt]].

This is a link to get the file [[File:YOH_nek5000.txt]].

= DINO =

== Step 1 ==

This is a link to get the file [[File:DINO_Step11b_dino.txt]].

== Step 2 ==

This is a link to get the file [[File:epsVStime.txt]].

This is a link to get the file [[File:kVStime.txt]].

This is a link to get the file [[File:Step2b_dino_space.txt]].

== Step 3 ==

This is a link to get the file [[File:Step13b_dino_time.txt]].

This is a link to get the file [[File:Step13b_dino_space.txt]].

== Step 4 ==

This is a link to get the file [[File:Step2b_dino_space_384.txt]].

This is a link to get the file [[File:Step2b_dino_space_512.txt]].

This is a link to get the file [[File:Step2b_dino_space_768.txt]].

This is a link to get the file [[File:Step2b_dino_time.txt]].

This is a link to get the file [[File:Step2b_dino_time_256.txt]].

This is a link to get the file [[File:Step2b_dino_time_384.txt]].

FileT 253:.txt

2020-09-21T21:00:50Z

Abdelsamie:

[[File:T_253.txt]]

FileT 253:.txt

2020-09-21T21:00:15Z

Abdelsamie:

[[File:T.253.txt]]

FileT 253:.txt

2020-09-21T20:59:42Z

Abdelsamie: Created page with "Media:T.253.txt"

[[Media:T.253.txt]]

File:T.txt

2020-09-21T20:52:22Z

Abdelsamie:

File:Profs.txt

2020-09-21T20:51:54Z

Abdelsamie:

File:HRR nek5000.txt

2020-09-21T20:50:34Z

Abdelsamie:

Results

2020-09-21T20:49:50Z

Abdelsamie: /* Step 4 */

The results of the Benchmark are organized as follows:

= Yales2 =

== Step 1 ==

This is a link to get the file [[File:Step11b_Ux_vs_x_10.0s_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step11b_Uy_vs_y_10.0s_CORIA_YALES2.txt]].

== Step 2 ==

This is a link to get the file [[File:Step2 YALES2 512 CFL0.10.txt]].

This is a link to get the file [[File:Step2 YALES2 512 CFL0.20.txt]].

This is a link to get the file [[File:Step2 YALES2 512 CFL0.30.txt]].

This is a link to get the file [[File:Step2 YALES2 512 CFL0.60.txt]].

This is a link to get the file [[File:Step12a_description_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step12b_12.11s_Ux_vs_x_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step12b_12.11s_Uy_vs_y_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step12b_12.11s_Wz_vs_x_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step12b_EPS_vs_t_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step12b_KE_vs_t_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step12c_scaling_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step12d_PressureConvergence_CORIA_YALES2.txt]].

== Step 3 ==

This is a link to get the file [[File:Step13a_description_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step13b_0.0ms_T_vs_x_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step13b_0.0ms_YH2_vs_x_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step13b_0.0ms_YO2_vs_x_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step13b_0.5ms_T_vs_y_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step13b_0.5ms_Ux_vs_x_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step13b_0.5ms_Uy_vs_y_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step13b_0.5ms_YH2_vs_y_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step13b_0.5ms_YO2_vs_y_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step13c_CORIA_YALES2.txt]].

== Step 4 ==

=== <math>256^3</math> ===

This is a link to get the file [[File:Step2b_0.0ms_T_vs_x_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step2b_0.0ms_YH2_vs_x_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step2b_0.0ms_YO2_vs_x_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step2b_0.5ms_HRR_vs_y_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step2b_0.5ms_T_vs_y_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step2b_0.5ms_Ux_vs_x_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step2b_0.5ms_Uy_vs_y_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step2b_0.5ms_YH2_vs_y_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step2b_0.5ms_YO2_vs_y_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step2b_0.5ms_YOH_vs_y_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step2b_P_vs_t_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step2b_Tmax_vs_t_CORIA_YALES2.txt]].

=== <math>384^3</math> ===

This is a link to get the file [[File:Step2b_0.0ms_T_vs_x_CORIA_YALES2_384.txt]].

This is a link to get the file [[File:Step2b_0.0ms_YH2_vs_x_CORIA_YALES2_384.txt]].

This is a link to get the file [[File:Step2b_0.0ms_YO2_vs_x_CORIA_YALES2_384.txt]].

This is a link to get the file [[File:Step2b_0.5ms_HRR_vs_y_CORIA_YALES2_384.txt]].

This is a link to get the file [[File:Step2b_0.5ms_T_vs_y_CORIA_YALES2_384.txt]].

This is a link to get the file [[File:Step2b_0.5ms_Ux_vs_x_CORIA_YALES2_384.txt]].

This is a link to get the file [[File:Step2b_0.5ms_Uy_vs_y_CORIA_YALES2_384.txt]].

This is a link to get the file [[File:Step2b_0.5ms_YH2_vs_y_CORIA_YALES2_384.txt]].

This is a link to get the file [[File:Step2b_0.5ms_YO2_vs_y_CORIA_YALES2_384.txt]].

This is a link to get the file [[File:Step2b_0.5ms_YOH_vs_y_CORIA_YALES2_384.txt]].

This is a link to get the file [[File:Step2b_P_vs_t_CORIA_YALES2_384.txt]].

This is a link to get the file [[File:Step2b_Tmax_vs_t_CORIA_YALES2_384.txt]].

=== <math>512^3</math> ===

This is a link to get the file [[File:Step2b_0.0ms_T_vs_x_CORIA_YALES2_512.txt]].

This is a link to get the file [[File:Step2b_0.0ms_YH2_vs_x_CORIA_YALES2_512.txt]].

This is a link to get the file [[File:Step2b_0.0ms_YO2_vs_x_CORIA_YALES2_512.txt]].

This is a link to get the file [[File:Step2b_0.5ms_HRR_vs_y_CORIA_YALES2_512.txt]].

This is a link to get the file [[File:Step2b_0.5ms_T_vs_y_CORIA_YALES2_512.txt]].

This is a link to get the file [[File:Step2b_0.5ms_Ux_vs_x_CORIA_YALES2_512.txt]].

This is a link to get the file [[File:Step2b_0.5ms_Uy_vs_y_CORIA_YALES2_512.txt]].

This is a link to get the file [[File:Step2b_0.5ms_YH2_vs_y_CORIA_YALES2_512.txt]].

This is a link to get the file [[File:Step2b_0.5ms_YO2_vs_y_CORIA_YALES2_512.txt]].

This is a link to get the file [[File:Step2b_0.5ms_YOH_vs_y_CORIA_YALES2_512.txt]].

This is a link to get the file [[File:Step2b_P_vs_t_CORIA_YALES2_512.txt]].

This is a link to get the file [[File:Step2b_Tmax_vs_t_CORIA_YALES2_512.txt]].

= Nek5000 =

== Step 1 ==

This is a link to get the file [[File:NEK500_Step1_Ux_vs_x_t10.txt]].

This is a link to get the file [[File:NEK500_Step1_Uy_vs_y_t10.txt]].

== Step 2 ==

This is a link to get the file [[File:Step12a_ETH.txt]].

This is a link to get the file [[File:Step12b_ETH_t9.33864.txt]].

This is a link to get the file [[File:Step12b_ETH_t12.11.txt]].

This is a link to get the file [[File:Step12b_ETH_t12.11_space.txt]].

This is a link to get the file [[File:Step12b_ETH_t12.11_time.txt]].

This is a link to get the file [[File:Step12c_ETH.txt]].

== Step 3 ==

This is a link to get the file [[File:Step13a_ETH.txt]].

This is a link to get the file [[File:Step13b_ETH.txt]].

This is a link to get the file [[File:Step13b_ETH_space.txt]].

This is a link to get the file [[File:Step13b_ETH_time.txt]].

This is a link to get the file [[File:Step13c_ETH.txt]].

== Step 4 ==

This is a link to get the file [[File:HRR_253.txt]].

This is a link to get the file [[File:HRR_514.txt]].

This is a link to get the file [[File:HRR_nek5000.txt]].

This is a link to get the file [[File:profs.txt]].

This is a link to get the file [[File:T.txt]].

This is a link to get the file [[FileT_253:.txt]].

This is a link to get the file [[File:T_514.txt]].

This is a link to get the file [[File:T_nek5000.txt]].

This is a link to get the file [[File:Vx_253.txt]].

This is a link to get the file [[File:Vx_514.txt]].

This is a link to get the file [[File:Vx_nek5000.txt]].

This is a link to get the file [[File:Vy_253.txt]].

This is a link to get the file [[File:Vy_514.txt]].

This is a link to get the file [[File:Vy_nek5000.txt]].

This is a link to get the file [[File:YH2_253.txt]].

This is a link to get the file [[File:YH2_514.txt]].

This is a link to get the file [[File:YH2_nek5000.txt]].

This is a link to get the file [[File:YO2_253.txt]].

This is a link to get the file [[File:YO2_514.txt]].

This is a link to get the file [[File:YO2_nek5000.txt]].

This is a link to get the file [[File:YOH_253.txt]].

This is a link to get the file [[File:YOH_514.txt]].

This is a link to get the file [[File:YOH_nek5000.txt]].

= DINO =

== Step 1 ==

This is a link to get the file [[File:DINO_Step11b_dino.txt]].

== Step 2 ==

This is a link to get the file [[File:epsVStime.txt]].

This is a link to get the file [[File:kVStime.txt]].

This is a link to get the file [[File:Step2b_dino_space.txt]].

== Step 3 ==

This is a link to get the file [[File:Step13b_dino_time.txt]].

This is a link to get the file [[File:Step13b_dino_space.txt]].

== Step 4 ==

This is a link to get the file [[File:Step2b_dino_space_384.txt]].

This is a link to get the file [[File:Step2b_dino_space_512.txt]].

This is a link to get the file [[File:Step2b_dino_space_768.txt]].

This is a link to get the file [[File:Step2b_dino_time.txt]].

This is a link to get the file [[File:Step2b_dino_time_256.txt]].

This is a link to get the file [[File:Step2b_dino_time_384.txt]].

File:HRR 514.txt

2020-09-21T20:46:00Z

Abdelsamie:

Results

2020-09-21T20:45:08Z

Abdelsamie: /* Step 4 */

The results of the Benchmark are organized as follows:

= Yales2 =

== Step 1 ==

This is a link to get the file [[File:Step11b_Ux_vs_x_10.0s_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step11b_Uy_vs_y_10.0s_CORIA_YALES2.txt]].

== Step 2 ==

This is a link to get the file [[File:Step2 YALES2 512 CFL0.10.txt]].

This is a link to get the file [[File:Step2 YALES2 512 CFL0.20.txt]].

This is a link to get the file [[File:Step2 YALES2 512 CFL0.30.txt]].

This is a link to get the file [[File:Step2 YALES2 512 CFL0.60.txt]].

This is a link to get the file [[File:Step12a_description_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step12b_12.11s_Ux_vs_x_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step12b_12.11s_Uy_vs_y_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step12b_12.11s_Wz_vs_x_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step12b_EPS_vs_t_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step12b_KE_vs_t_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step12c_scaling_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step12d_PressureConvergence_CORIA_YALES2.txt]].

== Step 3 ==

This is a link to get the file [[File:Step13a_description_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step13b_0.0ms_T_vs_x_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step13b_0.0ms_YH2_vs_x_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step13b_0.0ms_YO2_vs_x_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step13b_0.5ms_T_vs_y_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step13b_0.5ms_Ux_vs_x_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step13b_0.5ms_Uy_vs_y_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step13b_0.5ms_YH2_vs_y_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step13b_0.5ms_YO2_vs_y_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step13c_CORIA_YALES2.txt]].

== Step 4 ==

=== <math>256^3</math> ===

This is a link to get the file [[File:Step2b_0.0ms_T_vs_x_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step2b_0.0ms_YH2_vs_x_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step2b_0.0ms_YO2_vs_x_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step2b_0.5ms_HRR_vs_y_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step2b_0.5ms_T_vs_y_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step2b_0.5ms_Ux_vs_x_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step2b_0.5ms_Uy_vs_y_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step2b_0.5ms_YH2_vs_y_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step2b_0.5ms_YO2_vs_y_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step2b_0.5ms_YOH_vs_y_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step2b_P_vs_t_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step2b_Tmax_vs_t_CORIA_YALES2.txt]].

=== <math>384^3</math> ===

This is a link to get the file [[File:Step2b_0.0ms_T_vs_x_CORIA_YALES2_384.txt]].

This is a link to get the file [[File:Step2b_0.0ms_YH2_vs_x_CORIA_YALES2_384.txt]].

This is a link to get the file [[File:Step2b_0.0ms_YO2_vs_x_CORIA_YALES2_384.txt]].

This is a link to get the file [[File:Step2b_0.5ms_HRR_vs_y_CORIA_YALES2_384.txt]].

This is a link to get the file [[File:Step2b_0.5ms_T_vs_y_CORIA_YALES2_384.txt]].

This is a link to get the file [[File:Step2b_0.5ms_Ux_vs_x_CORIA_YALES2_384.txt]].

This is a link to get the file [[File:Step2b_0.5ms_Uy_vs_y_CORIA_YALES2_384.txt]].

This is a link to get the file [[File:Step2b_0.5ms_YH2_vs_y_CORIA_YALES2_384.txt]].

This is a link to get the file [[File:Step2b_0.5ms_YO2_vs_y_CORIA_YALES2_384.txt]].

This is a link to get the file [[File:Step2b_0.5ms_YOH_vs_y_CORIA_YALES2_384.txt]].

This is a link to get the file [[File:Step2b_P_vs_t_CORIA_YALES2_384.txt]].

This is a link to get the file [[File:Step2b_Tmax_vs_t_CORIA_YALES2_384.txt]].

=== <math>512^3</math> ===

This is a link to get the file [[File:Step2b_0.0ms_T_vs_x_CORIA_YALES2_512.txt]].

This is a link to get the file [[File:Step2b_0.0ms_YH2_vs_x_CORIA_YALES2_512.txt]].

This is a link to get the file [[File:Step2b_0.0ms_YO2_vs_x_CORIA_YALES2_512.txt]].

This is a link to get the file [[File:Step2b_0.5ms_HRR_vs_y_CORIA_YALES2_512.txt]].

This is a link to get the file [[File:Step2b_0.5ms_T_vs_y_CORIA_YALES2_512.txt]].

This is a link to get the file [[File:Step2b_0.5ms_Ux_vs_x_CORIA_YALES2_512.txt]].

This is a link to get the file [[File:Step2b_0.5ms_Uy_vs_y_CORIA_YALES2_512.txt]].

This is a link to get the file [[File:Step2b_0.5ms_YH2_vs_y_CORIA_YALES2_512.txt]].

This is a link to get the file [[File:Step2b_0.5ms_YO2_vs_y_CORIA_YALES2_512.txt]].

This is a link to get the file [[File:Step2b_0.5ms_YOH_vs_y_CORIA_YALES2_512.txt]].

This is a link to get the file [[File:Step2b_P_vs_t_CORIA_YALES2_512.txt]].

This is a link to get the file [[File:Step2b_Tmax_vs_t_CORIA_YALES2_512.txt]].

= Nek5000 =

== Step 1 ==

This is a link to get the file [[File:NEK500_Step1_Ux_vs_x_t10.txt]].

This is a link to get the file [[File:NEK500_Step1_Uy_vs_y_t10.txt]].

== Step 2 ==

This is a link to get the file [[File:Step12a_ETH.txt]].

This is a link to get the file [[File:Step12b_ETH_t9.33864.txt]].

This is a link to get the file [[File:Step12b_ETH_t12.11.txt]].

This is a link to get the file [[File:Step12b_ETH_t12.11_space.txt]].

This is a link to get the file [[File:Step12b_ETH_t12.11_time.txt]].

This is a link to get the file [[File:Step12c_ETH.txt]].

== Step 3 ==

This is a link to get the file [[File:Step13a_ETH.txt]].

This is a link to get the file [[File:Step13b_ETH.txt]].

This is a link to get the file [[File:Step13b_ETH_space.txt]].

This is a link to get the file [[File:Step13b_ETH_time.txt]].

This is a link to get the file [[File:Step13c_ETH.txt]].

== Step 4 ==

This is a link to get the file [[File:HRR_253.txt]].

This is a link to get the file [[File:HRR_514.txt]].

This is a link to get the file [[File:HRR_nek5000.dat]].

This is a link to get the file [[File:profs.dat]].

This is a link to get the file [[File:T.dat]].

This is a link to get the file [[FileT_253:.dat]].

This is a link to get the file [[File:T_514.dat]].

This is a link to get the file [[File:T_nek5000.dat]].

This is a link to get the file [[File:Vx_253.dat]].

This is a link to get the file [[File:Vx_514.dat]].

This is a link to get the file [[File:Vx_nek5000.dat]].

This is a link to get the file [[File:Vy_253.dat]].

This is a link to get the file [[File:Vy_514.dat]].

This is a link to get the file [[File:Vy_nek5000.dat]].

This is a link to get the file [[File:YH2_253.dat]].

This is a link to get the file [[File:YH2_514.dat]].

This is a link to get the file [[File:YH2_nek5000.dat]].

This is a link to get the file [[File:YO2_253.dat]].

This is a link to get the file [[File:YO2_514.dat]].

This is a link to get the file [[File:YO2_nek5000.dat]].

This is a link to get the file [[File:YOH_253.dat]].

This is a link to get the file [[File:YOH_514.dat]].

This is a link to get the file [[File:YOH_nek5000.dat]].

= DINO =

== Step 1 ==

This is a link to get the file [[File:DINO_Step11b_dino.txt]].

== Step 2 ==

This is a link to get the file [[File:epsVStime.txt]].

This is a link to get the file [[File:kVStime.txt]].

This is a link to get the file [[File:Step2b_dino_space.txt]].

== Step 3 ==

This is a link to get the file [[File:Step13b_dino_time.txt]].

This is a link to get the file [[File:Step13b_dino_space.txt]].

== Step 4 ==

This is a link to get the file [[File:Step2b_dino_space_384.txt]].

This is a link to get the file [[File:Step2b_dino_space_512.txt]].

This is a link to get the file [[File:Step2b_dino_space_768.txt]].

This is a link to get the file [[File:Step2b_dino_time.txt]].

This is a link to get the file [[File:Step2b_dino_time_256.txt]].

This is a link to get the file [[File:Step2b_dino_time_384.txt]].

File:HRR 253.txt

2020-09-21T20:44:32Z

Abdelsamie: Abdelsamie uploaded a new version of File:HRR 253.txt

File:HRR 253.txt

2020-09-21T20:43:21Z

Abdelsamie:

File:KVStime.txt

2020-09-16T16:01:17Z

Abdelsamie:

Results

2020-09-16T16:00:41Z

Abdelsamie: /* Step 2 */

The results of the Benchmark are organized as follows:

= Yales2 =

== Step 1 ==

This is a link to get the file [[File:Step11b_Ux_vs_x_10.0s_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step11b_Uy_vs_y_10.0s_CORIA_YALES2.txt]].

== Step 2 ==

This is a link to get the file [[File:Step2 YALES2 512 CFL0.10.txt]].

This is a link to get the file [[File:Step2 YALES2 512 CFL0.20.txt]].

This is a link to get the file [[File:Step2 YALES2 512 CFL0.30.txt]].

This is a link to get the file [[File:Step2 YALES2 512 CFL0.60.txt]].

This is a link to get the file [[File:Step12a_description_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step12b_12.11s_Ux_vs_x_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step12b_12.11s_Uy_vs_y_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step12b_12.11s_Wz_vs_x_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step12b_EPS_vs_t_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step12b_KE_vs_t_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step12c_scaling_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step12d_PressureConvergence_CORIA_YALES2.txt]].

== Step 3 ==

This is a link to get the file [[File:Step13a_description_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step13b_0.0ms_T_vs_x_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step13b_0.0ms_YH2_vs_x_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step13b_0.0ms_YO2_vs_x_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step13b_0.5ms_T_vs_y_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step13b_0.5ms_Ux_vs_x_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step13b_0.5ms_Uy_vs_y_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step13b_0.5ms_YH2_vs_y_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step13b_0.5ms_YO2_vs_y_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step13c_CORIA_YALES2.txt]].

== Step 4 ==

=== <math>256^3</math> ===

This is a link to get the file [[File:Step2b_0.0ms_T_vs_x_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step2b_0.0ms_YH2_vs_x_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step2b_0.0ms_YO2_vs_x_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step2b_0.5ms_HRR_vs_y_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step2b_0.5ms_T_vs_y_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step2b_0.5ms_Ux_vs_x_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step2b_0.5ms_Uy_vs_y_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step2b_0.5ms_YH2_vs_y_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step2b_0.5ms_YO2_vs_y_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step2b_0.5ms_YOH_vs_y_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step2b_P_vs_t_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step2b_Tmax_vs_t_CORIA_YALES2.txt]].

=== <math>384^3</math> ===

This is a link to get the file [[File:Step2b_0.0ms_T_vs_x_CORIA_YALES2_384.txt]].

This is a link to get the file [[File:Step2b_0.0ms_YH2_vs_x_CORIA_YALES2_384.txt]].

This is a link to get the file [[File:Step2b_0.0ms_YO2_vs_x_CORIA_YALES2_384.txt]].

This is a link to get the file [[File:Step2b_0.5ms_HRR_vs_y_CORIA_YALES2_384.txt]].

This is a link to get the file [[File:Step2b_0.5ms_T_vs_y_CORIA_YALES2_384.txt]].

This is a link to get the file [[File:Step2b_0.5ms_Ux_vs_x_CORIA_YALES2_384.txt]].

This is a link to get the file [[File:Step2b_0.5ms_Uy_vs_y_CORIA_YALES2_384.txt]].

This is a link to get the file [[File:Step2b_0.5ms_YH2_vs_y_CORIA_YALES2_384.txt]].

This is a link to get the file [[File:Step2b_0.5ms_YO2_vs_y_CORIA_YALES2_384.txt]].

This is a link to get the file [[File:Step2b_0.5ms_YOH_vs_y_CORIA_YALES2_384.txt]].

This is a link to get the file [[File:Step2b_P_vs_t_CORIA_YALES2_384.txt]].

This is a link to get the file [[File:Step2b_Tmax_vs_t_CORIA_YALES2_384.txt]].

=== <math>512^3</math> ===

This is a link to get the file [[File:Step2b_0.0ms_T_vs_x_CORIA_YALES2_512.txt]].

This is a link to get the file [[File:Step2b_0.0ms_YH2_vs_x_CORIA_YALES2_512.txt]].

This is a link to get the file [[File:Step2b_0.0ms_YO2_vs_x_CORIA_YALES2_512.txt]].

This is a link to get the file [[File:Step2b_0.5ms_HRR_vs_y_CORIA_YALES2_512.txt]].

This is a link to get the file [[File:Step2b_0.5ms_T_vs_y_CORIA_YALES2_512.txt]].

This is a link to get the file [[File:Step2b_0.5ms_Ux_vs_x_CORIA_YALES2_512.txt]].

This is a link to get the file [[File:Step2b_0.5ms_Uy_vs_y_CORIA_YALES2_512.txt]].

This is a link to get the file [[File:Step2b_0.5ms_YH2_vs_y_CORIA_YALES2_512.txt]].

This is a link to get the file [[File:Step2b_0.5ms_YO2_vs_y_CORIA_YALES2_512.txt]].

This is a link to get the file [[File:Step2b_0.5ms_YOH_vs_y_CORIA_YALES2_512.txt]].

This is a link to get the file [[File:Step2b_P_vs_t_CORIA_YALES2_512.txt]].

This is a link to get the file [[File:Step2b_Tmax_vs_t_CORIA_YALES2_512.txt]].

= Nek5000 =

== Step 1 ==

This is a link to get the file [[File:NEK500_Step1_Ux_vs_x_t10.txt]].

This is a link to get the file [[File:NEK500_Step1_Uy_vs_y_t10.txt]].

== Step 2 ==

This is a link to get the file [[File:Step12a_ETH.txt]].

This is a link to get the file [[File:Step12b_ETH_t9.33864.txt]].

This is a link to get the file [[File:Step12b_ETH_t12.11.txt]].

This is a link to get the file [[File:Step12b_ETH_t12.11_space.txt]].

This is a link to get the file [[File:Step12b_ETH_t12.11_time.txt]].

This is a link to get the file [[File:Step12c_ETH.txt]].

== Step 3 ==

This is a link to get the file [[File:Step13a_ETH.txt]].

This is a link to get the file [[File:Step13b_ETH.txt]].

This is a link to get the file [[File:Step13b_ETH_space.txt]].

This is a link to get the file [[File:Step13b_ETH_time.txt]].

This is a link to get the file [[File:Step13c_ETH.txt]].

== Step 4 ==

This is a link to get the file [[File:HRR_253.dat]].

This is a link to get the file [[File:HRR_514.dat]].

This is a link to get the file [[File:HRR_nek5000.dat]].

This is a link to get the file [[File:profs.dat]].

This is a link to get the file [[File:T.dat]].

This is a link to get the file [[FileT_253:.dat]].

This is a link to get the file [[File:T_514.dat]].

This is a link to get the file [[File:T_nek5000.dat]].

This is a link to get the file [[File:Vx_253.dat]].

This is a link to get the file [[File:Vx_514.dat]].

This is a link to get the file [[File:Vx_nek5000.dat]].

This is a link to get the file [[File:Vy_253.dat]].

This is a link to get the file [[File:Vy_514.dat]].

This is a link to get the file [[File:Vy_nek5000.dat]].

This is a link to get the file [[File:YH2_253.dat]].

This is a link to get the file [[File:YH2_514.dat]].

This is a link to get the file [[File:YH2_nek5000.dat]].

This is a link to get the file [[File:YO2_253.dat]].

This is a link to get the file [[File:YO2_514.dat]].

This is a link to get the file [[File:YO2_nek5000.dat]].

This is a link to get the file [[File:YOH_253.dat]].

This is a link to get the file [[File:YOH_514.dat]].

This is a link to get the file [[File:YOH_nek5000.dat]].

= DINO =

== Step 1 ==

This is a link to get the file [[File:DINO_Step11b_dino.txt]].

== Step 2 ==

This is a link to get the file [[File:epsVStime.txt]].

This is a link to get the file [[File:kVStime.txt]].

This is a link to get the file [[File:Step2b_dino_space.txt]].

== Step 3 ==

This is a link to get the file [[File:Step13b_dino_time.txt]].

This is a link to get the file [[File:Step13b_dino_space.txt]].

== Step 4 ==

This is a link to get the file [[File:Step2b_dino_space_384.txt]].

This is a link to get the file [[File:Step2b_dino_space_512.txt]].

This is a link to get the file [[File:Step2b_dino_space_768.txt]].

This is a link to get the file [[File:Step2b_dino_time.txt]].

This is a link to get the file [[File:Step2b_dino_time_256.txt]].

This is a link to get the file [[File:Step2b_dino_time_384.txt]].

Results

2020-09-16T15:57:53Z

Abdelsamie: /* Step 2 */

The results of the Benchmark are organized as follows:

= Yales2 =

== Step 1 ==

This is a link to get the file [[File:Step11b_Ux_vs_x_10.0s_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step11b_Uy_vs_y_10.0s_CORIA_YALES2.txt]].

== Step 2 ==

This is a link to get the file [[File:Step2 YALES2 512 CFL0.10.txt]].

This is a link to get the file [[File:Step2 YALES2 512 CFL0.20.txt]].

This is a link to get the file [[File:Step2 YALES2 512 CFL0.30.txt]].

This is a link to get the file [[File:Step2 YALES2 512 CFL0.60.txt]].

This is a link to get the file [[File:Step12a_description_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step12b_12.11s_Ux_vs_x_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step12b_12.11s_Uy_vs_y_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step12b_12.11s_Wz_vs_x_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step12b_EPS_vs_t_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step12b_KE_vs_t_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step12c_scaling_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step12d_PressureConvergence_CORIA_YALES2.txt]].

== Step 3 ==

This is a link to get the file [[File:Step13a_description_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step13b_0.0ms_T_vs_x_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step13b_0.0ms_YH2_vs_x_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step13b_0.0ms_YO2_vs_x_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step13b_0.5ms_T_vs_y_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step13b_0.5ms_Ux_vs_x_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step13b_0.5ms_Uy_vs_y_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step13b_0.5ms_YH2_vs_y_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step13b_0.5ms_YO2_vs_y_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step13c_CORIA_YALES2.txt]].

== Step 4 ==

=== <math>256^3</math> ===

This is a link to get the file [[File:Step2b_0.0ms_T_vs_x_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step2b_0.0ms_YH2_vs_x_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step2b_0.0ms_YO2_vs_x_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step2b_0.5ms_HRR_vs_y_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step2b_0.5ms_T_vs_y_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step2b_0.5ms_Ux_vs_x_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step2b_0.5ms_Uy_vs_y_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step2b_0.5ms_YH2_vs_y_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step2b_0.5ms_YO2_vs_y_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step2b_0.5ms_YOH_vs_y_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step2b_P_vs_t_CORIA_YALES2.txt]].

This is a link to get the file [[File:Step2b_Tmax_vs_t_CORIA_YALES2.txt]].

=== <math>384^3</math> ===

This is a link to get the file [[File:Step2b_0.0ms_T_vs_x_CORIA_YALES2_384.txt]].

This is a link to get the file [[File:Step2b_0.0ms_YH2_vs_x_CORIA_YALES2_384.txt]].

This is a link to get the file [[File:Step2b_0.0ms_YO2_vs_x_CORIA_YALES2_384.txt]].

This is a link to get the file [[File:Step2b_0.5ms_HRR_vs_y_CORIA_YALES2_384.txt]].

This is a link to get the file [[File:Step2b_0.5ms_T_vs_y_CORIA_YALES2_384.txt]].

This is a link to get the file [[File:Step2b_0.5ms_Ux_vs_x_CORIA_YALES2_384.txt]].

This is a link to get the file [[File:Step2b_0.5ms_Uy_vs_y_CORIA_YALES2_384.txt]].

This is a link to get the file [[File:Step2b_0.5ms_YH2_vs_y_CORIA_YALES2_384.txt]].

This is a link to get the file [[File:Step2b_0.5ms_YO2_vs_y_CORIA_YALES2_384.txt]].

This is a link to get the file [[File:Step2b_0.5ms_YOH_vs_y_CORIA_YALES2_384.txt]].

This is a link to get the file [[File:Step2b_P_vs_t_CORIA_YALES2_384.txt]].

This is a link to get the file [[File:Step2b_Tmax_vs_t_CORIA_YALES2_384.txt]].

=== <math>512^3</math> ===

This is a link to get the file [[File:Step2b_0.0ms_T_vs_x_CORIA_YALES2_512.txt]].

This is a link to get the file [[File:Step2b_0.0ms_YH2_vs_x_CORIA_YALES2_512.txt]].

This is a link to get the file [[File:Step2b_0.0ms_YO2_vs_x_CORIA_YALES2_512.txt]].

This is a link to get the file [[File:Step2b_0.5ms_HRR_vs_y_CORIA_YALES2_512.txt]].

This is a link to get the file [[File:Step2b_0.5ms_T_vs_y_CORIA_YALES2_512.txt]].

This is a link to get the file [[File:Step2b_0.5ms_Ux_vs_x_CORIA_YALES2_512.txt]].

This is a link to get the file [[File:Step2b_0.5ms_Uy_vs_y_CORIA_YALES2_512.txt]].

This is a link to get the file [[File:Step2b_0.5ms_YH2_vs_y_CORIA_YALES2_512.txt]].

This is a link to get the file [[File:Step2b_0.5ms_YO2_vs_y_CORIA_YALES2_512.txt]].

This is a link to get the file [[File:Step2b_0.5ms_YOH_vs_y_CORIA_YALES2_512.txt]].

This is a link to get the file [[File:Step2b_P_vs_t_CORIA_YALES2_512.txt]].

This is a link to get the file [[File:Step2b_Tmax_vs_t_CORIA_YALES2_512.txt]].

= Nek5000 =

== Step 1 ==

This is a link to get the file [[File:NEK500_Step1_Ux_vs_x_t10.txt]].

This is a link to get the file [[File:NEK500_Step1_Uy_vs_y_t10.txt]].

== Step 2 ==

This is a link to get the file [[File:Step12a_ETH.txt]].

This is a link to get the file [[File:Step12b_ETH_t9.33864.txt]].

This is a link to get the file [[File:Step12b_ETH_t12.11.txt]].

This is a link to get the file [[File:Step12b_ETH_t12.11_space.txt]].

This is a link to get the file [[File:Step12b_ETH_t12.11_time.txt]].

This is a link to get the file [[File:Step12c_ETH.txt]].

== Step 3 ==

This is a link to get the file [[File:Step13a_ETH.txt]].

This is a link to get the file [[File:Step13b_ETH.txt]].

This is a link to get the file [[File:Step13b_ETH_space.txt]].

This is a link to get the file [[File:Step13b_ETH_time.txt]].

This is a link to get the file [[File:Step13c_ETH.txt]].

== Step 4 ==

This is a link to get the file [[File:HRR_253.dat]].

This is a link to get the file [[File:HRR_514.dat]].

This is a link to get the file [[File:HRR_nek5000.dat]].

This is a link to get the file [[File:profs.dat]].

This is a link to get the file [[File:T.dat]].

This is a link to get the file [[FileT_253:.dat]].

This is a link to get the file [[File:T_514.dat]].

This is a link to get the file [[File:T_nek5000.dat]].

This is a link to get the file [[File:Vx_253.dat]].

This is a link to get the file [[File:Vx_514.dat]].

This is a link to get the file [[File:Vx_nek5000.dat]].

This is a link to get the file [[File:Vy_253.dat]].

This is a link to get the file [[File:Vy_514.dat]].

This is a link to get the file [[File:Vy_nek5000.dat]].

This is a link to get the file [[File:YH2_253.dat]].

This is a link to get the file [[File:YH2_514.dat]].

This is a link to get the file [[File:YH2_nek5000.dat]].

This is a link to get the file [[File:YO2_253.dat]].

This is a link to get the file [[File:YO2_514.dat]].

This is a link to get the file [[File:YO2_nek5000.dat]].

This is a link to get the file [[File:YOH_253.dat]].

This is a link to get the file [[File:YOH_514.dat]].

This is a link to get the file [[File:YOH_nek5000.dat]].

= DINO =

== Step 1 ==

This is a link to get the file [[File:DINO_Step11b_dino.txt]].

== Step 2 ==

This is a link to get the file [[File:epsVStime.txt]].

This is a link to get the file [[File:kVStime.dat]].

This is a link to get the file [[File:Step2b_dino_space.txt]].

== Step 3 ==

This is a link to get the file [[File:Step13b_dino_time.txt]].

This is a link to get the file [[File:Step13b_dino_space.txt]].

== Step 4 ==

This is a link to get the file [[File:Step2b_dino_space_384.txt]].

This is a link to get the file [[File:Step2b_dino_space_512.txt]].

This is a link to get the file [[File:Step2b_dino_space_768.txt]].

This is a link to get the file [[File:Step2b_dino_time.txt]].

This is a link to get the file [[File:Step2b_dino_time_256.txt]].

This is a link to get the file [[File:Step2b_dino_time_384.txt]].

File:EpsVStime.txt

2020-09-16T15:55:21Z

Abdelsamie: Abdelsamie uploaded a new version of File:EpsVStime.txt

File:EpsVStime.txt

2020-09-16T15:54:24Z

Abdelsamie:

Codes

2020-09-16T15:26:52Z

Abdelsamie: /* General comments on the codes */

= Code Description =

This page is dedicated to a short presentation of the three '''low-Mach number''' codes used for the rest of this benchmarl: [https://www.coria-cfd.fr/index.php/YALES2 YALES2], [http://www.lss.ovgu.de/lss/en/Research/Computational+Fluid+Dynamics.html DINO] and [http://nek5000.mcs.anl.gov Nek5000].

Since these codes have already been the subject of many publications and are not completely new, '''only the most relevant features are discussed in what follows''', with suitable references for those readers needing more details.

== YALES2 ==

YALES2 is a '''massively parallel multiphysics platform'''<ref name="moureau2011"/> developed since 2009 by Moureau, Lartigue and co-workers at CORIA (Rouen, France).
It is dedicated to the high-fidelity simulation of '''low-Mach number flows in complex geometries'''.
It is based on the '''Finite Volumes formulation''' of the '''Navier-Stokes equations''' and it can solve both '''non-reacting''' and '''reacting flows'''.
It can actually solve various physical problems thanks to its original structure which is composed of a main numerical library accompanied with tens of dedicated solvers (for acoustics, multiphase flows, heat transfer, radiation\ldots) which can be coupled with one another.
YALES2 relies on '''unstructured meshes''' and a '''fully parallel dynamic mesh adaptation technique''' to improve the resolution in physically-relevant zones to mitigate the computational cost<ref name="benard2015"/>.
As a result it can easily handle meshes composed of billions of tetrahedra, thus enabling the '''Direct Numerical Simulation''' of laboratory and semi-industrial configurations.
It is now composed of nearly 500,000 lines of object-oriented Fortran and the parallelism is currently ensured by a pure '''MPI''' paradigm, although a hybrid '''OpenMP/MPI''' as well as a GPU version are under development.

As most low-Mach number codes, the time-advancement is based on a '''projection-correction method''' following the pioneering work of<ref name="chorin1968"/>.
The prediction step uses a method which is a blend between a '''4th-order Runge-Kutta method''' and a '''4th-order Lax-Wendroff-like method'''<ref name="kraushaar2011"/>, combined with a '''4th-order node-based centered finite-volume discretization''' of the convective and diffusive terms.
Moreover, to improve the performance of the correction step, the pressure of the previous iteration is included in the prediction step to limit the '''splitting errors'''.
The correction step is required to ensure '''mass conservation''', using a pressure that arises from a '''Poisson equation'''.
This is performed numerically by solving a linear system on the pressure at each node of the mesh thanks to a dedicated in-house version of the deflated conjugate gradient algorithm, which has been optimized for solving elliptic equations on massively parallel machines<ref name="malandain2013"/>.

When considering '''multispecies''' and '''non-isothermal flows''', the extension of the classical projection method proposed by Pierce et al.<ref name="pierce2004"/> is used to account for '''variable-density flows'''.
All the thermodynamic and transport properties are provided by the '''Cantera software'''<ref name="goodwin2003"/>, which has been fully re-implemented in '''Fortran''' to avoid any performance issues.
Each species thermodynamic property is specified by '''5th-order polynomials''' on two temperature ranges (below and above 1000 K).
The mixture is supposed to be both thermally and mechanically perfect.

Regarding transport properties, several type of models are implemented in YALES2:

1) the default approach is based on the computation of transport properties for each species (using tabulated molecular potentials), then combining those to obtain mixture-averaged coefficients for '''viscosity''', '''conductivity''' and '''diffusion velocities''' (Hirschfelder and Curtiss approximation<ref name="hirschfelder1964"/>;

2) alternatively, simplified laws (for example the Sutherland law<ref name="sutherland1893"/> can be used for the '''viscosity''', while fixed values for '''Prandtl''' and '''Schmidt numbers''' allow the computation of '''conductivity''' and '''diffusion coefficients''';

3) a mix of both approaches, for example computing '''viscosity''' and '''conductivity''' with a mixture-averaged approximation and then imposing a '''Lewis number''' for each species.
This last approach has been retained in the present benchmark.

Finally, the source terms used in the '''reacting simulations''' are modeled with an '''Arrhenius law''' with the necessary modifications needed to take into account three-body or pressure-dependent reactions.

From a numerical point of view, it must be noticed that both the '''diffusion''' and '''reaction processes''' occur at time scales which can be orders of magnitude smaller than the convective time scale.
Solving these phenomena with explicit methods would thus drastically limit the '''global timestep''' of the whole simulation and induce an overwhelming CPU cost.
To mitigate these effects when dealing with '''multi-species reacting flows''', the classical operator '''splitting technique''' is used.
The '''diffusion process''' is solved with a fractional timestep method inside each convective iteration, each substep being limited by a '''Fourier condition''' to ensure stability.
This method gets activated only when the mesh is very fine (typically when performing DNS with very diffusive species like <math>H_2</math> or <math>H</math>, as in the present project); otherwise an explicit treatment is sufficient.
The chemical source terms are then integrated with a dedicated stiff solver, namely the '''CVODE''' library from SUNDIALS<ref name="cohen1996cvode"/><ref name="cvodeUG">A.C. Hindmarsh and R. Serban. User documentation for '''CVODE'''. [https://computing.llnl.gov/sites/default/files/public/cv_guide.pdf].</ref><ref name="sundials"/>.
To that purpose, each control volume is considered as an isolated reactor with both constant pressure and enthalpy.

Using the stiff integration technique results in a very strong load imbalance between the various regions of the flow: the fresh gases are solved in a very small number of integration steps while the inner flame region may require tens or even hundreds of integration steps.
To overcome this difficulty, a dedicated '''MPI''' dynamic scheduler based on a work-sharing algorithm ensures global load-balancing.

== DINO ==

DINO is a '''3-D DNS code''' used for '''incompressible''' or '''low-Mach number flows''', the latter approach being used in this project.
The development of DINO started in the group of D. Thévenin (Univ. of Magdeburg) in 2013.
DINO is a '''Fortran-90 code''', written on top of a 2-D pencil decomposition to enable efficient large-scale parallel simulations on distributed-memory supercomputers by coupling with the open-source library 2-DECOMP&FFT<ref name="li2010"/>.
The code offers different features and algorithms in order to investigate different physicochemical processes.
Spatial derivative are computed by default using '''sixth-order central finite differences'''.
Time integration relies on '''several Runge-Kutta solvers'''.
In what follows, an explicit '''4th-order Runge-Kutta approach''' has been used.
A '''3rd-order semi-implicit Runge-Kutta integration''' can be activated as needed, when considering stiff chemistry.
In this case, non-stiff terms are still computed with explicit Runge-Kutta, while the '''PyJac package'''<ref>Create analytical jacobian matrix source code for chemical kinetics.</ref> is used to integrate in an implicit manner all chemistry terms with an analytical Jacobian computation.
All thermodynamic, chemical and transport properties are computed using the open-source library '''Cantera 2.4.0'''<ref>Cantera.</ref>.

The transport properties can be computed based on three different models:

1) Constant Lewis numbers,

2) mixture-averaged,

3) full multicomponent diffusion, by coupling either again with '''Cantera''' or with the open-source library EGlib<ref name="ern1995"/>.

The '''Poisson equation''' is solved using Fast Fourier Transform ('''FFT''') for '''periodic''' as well as for '''non-periodic boundary conditions''', relying in the latter case on an in-house pre- and post-processing technique.
The I/O operations are implemented using two different approaches: (1) binary '''MPI-I/O''' using 2-DECOMP&FFT for check-points and restart files; (2) HDF5 files used for analysis and visualization.

'''Multi-phase flows''' can be simulated in DINO using resolved or non-resolved (point) particles and droplets using a '''Lagrangian approach'''<ref name="abdelsamie2019"/><ref name="abdelsamie2020"/>. Complex boundaries are represented by a novel second-order immersed boundary method implementation ('''IBM''') based on a directional extrapolation scheme<ref name="chi2020"/>.
More details about the implemented algorithms can be found in particular in<ref name="abdelsamie2016"/>.
Since DINO has been developed as a multi-purpose code for analyzing many different '''reacting''' and '''non-reacting flows'''<ref name="chi2018"/><ref name="oster2018"/><ref name="abdelsamie2019-2"/>, a detailed verification and validation is obviously essential.

== Nek5000 ==

This '''spectral element low-Mach number reacting flow solver''' is based on the highly-efficient open-source solver Nek5000<ref>Nek5000 version v17.0, Argonne National Laboratory, IL, U.S.A.</ref> extended by a plugin developed at ETH implementing a '''high-order splitting scheme''' for '''low-Mach number reacting flows'''<ref name="tomboulides1997"/>.
The spectral element method ('''SEM''') is a '''high-order weighted residual technique''' for spatial discretization that combines the accuracy of spectral methods with the geometric flexibility of the finite element method allowing for accurately representation of complex geometries<ref name="deville2002"/>.
The computational domain is decomposed into <math>E</math> conforming elements, which are '''quadrilaterals''' ('''in 2-D''') or '''hexahedra''' (in '''3-D''') that conform to the domain boundaries.
Within each element, functions are expanded as <math>N</math>th-order polynomials so that resolution can be increased either by decreasing the element size (<math>h</math>-type refinement) or by increasing the polynomial order (<math>p</math>-type refinement; typically <math>N = 7 - 15</math>).
The grids can be unstructured and allow for '''static local refinement''', while '''adaptive mesh refinement''' has been recently developed<ref name="tanarro2020"/>.
By casting the '''polynomial approximation''' in tensor-product form, the differential operators on <math>N^3</math> gridpoints per element can be evaluated with only <math>O(N^4)</math> work and <math>O(N^3)</math> storage.

The principal advantage of the '''SEM''' is that convergence is exponential in <math>N</math>, yielding minimal '''numerical dispersion''' and '''dissipation''', so that significantly fewer grid points per wavelength are required in order to accurately propagate a turbulent structure over the extended time required in high Reynolds number simulations.
Nek5000 uses locally '''structured basis coefficients''' (<math>N\times N \times N</math> arrays), which allow direct addressing and tensor-product-based derivative evaluation that can be cast as efficient matrix-matrix products involving <math>N^2</math> operators applied to <math>N^3</math> data values for each element.
As a result, data movement per grid point is the same as for '''low-order methods'''.
It uses scalable domain-decomposition-based iterative solvers with efficient preconditioners.
Communication is based on the Message Passing Interface ('''MPI''') standard, and the code has proven scalability to over one million ranks.
Nek5000 provides balanced I/O latency among all processors and reduces the overhead or even completely hides the I/O latency by using dedicated I/O communicators in the optimal case.

'''Time advancement''' is performed using the '''splitting scheme''' proposed in<ref name="tomboulides1997" /> to decouple the highly non-linear and stiff thermochemistry (species and energy governing equations) from the hydrodynamic system (continuity and momentum).
Species and energy equations are integrated without further '''splitting using the implicit stiff integrator solver CVODE from the SUNDIALS package'''<ref name="cohen1996cvode" /><ref name="cvodeUG" /><ref name="sundials" /> that uses backward differentiation formulas (BDF).
The '''continuity''' and '''momentum equations''' are integrated using a '''second-''' or '''third-order semi-implicit formulation''' (EXT/BDF) treating the non-linear advection term explicitly<ref name="deville2002" />.
The thermodynamic properties, detailed chemistry, and transport properties are provided by optimized subroutines compatible with '''Chemkin'''<ref name="chemkin"/>.

The reacting flow solver can handle complex time-varying geometries and has been used for instance to simulate laboratory-scale internal combustion engines<ref name="MS"/><ref name="TCC"/>.
It can account for conjugate fluid-solid heat transfer and detailed gas phase as well as surface kinetics<ref name="catalytic"/>.

== General comments on the codes ==

The three '''aforementioned solvers''' are all '''unsteady''', '''high-fidelity codes''' based on the '''low-Mach number''' formulation of the '''Navier-Stokes equations'''.
They can perform both '''Direct Numerical Simulations''' or '''Large Eddy Simulations''' of reacting flows, only '''DNS''' being considered here.
However, they differ in a certain number of points, mainly from the numerical point of view.
The aim of this section is to emphasize those major differences.
First, '''YALES2''' is an '''unstructured code''', designed to handle any type of elements; its main application field pertains to '''LES''' of industrially relevant flows, though '''DNS''' is possible as well.
On the other hand, both '''DINO''' and '''Nek5000''' are mostly dedicated to '''DNS''' of configurations found in fundamental research.
Both '''DINO''' and '''Nek5000''' can only deal with '''quads''' or '''hexas''', with the major difference that '''DINO''' is based on a '''structured connectivity''' while '''Nek5000''' can use '''unstructured meshes''' (pavings).
As a consequence, both '''DINO''' and '''Nek5000''' employ '''higher-order numerical schemes''' compared to '''YALES2''', limited at best to a '''4th-order scheme'''.
All codes rely on dedicated libraries to compute the thermo-chemical properties of the flow, either '''Chemkin''', '''Cantera''', or in-house versions of those.
Moreover, they also rely at least to some extent on external software to perform the temporal integration of the stiff chemical source terms.
Regarding the Poisson equation for pressure which must be solved by all codes, '''DINO''' relies on a spectral formulation by performing direct and inverse Fourier transforms, which is possible thanks to its structured mesh.
On the other hand, both '''YALES2''' and '''Nek5000''' use an iterative solver with an efficient preconditioning technique; this method is more versatile and should be computationally more efficient for large and complex geometrical configurations.
'''Nek5000''' employs CVODE to integrate the thermochemical equations without further '''splitting''' of the different terms accounting for convection, diffusion and chemistry.
The main differences between the three codes are summarized in the table below.
Please note that the presented values are those used for the benchmark, even though some other options are available in each codes.

{| class="wikitable alternance center"
|+ Table 1: Major numerical properties of the three high-fidelity codes as used in this benchmark
|-
! scope="col" | Code
! scope="col" | YALES2
! scope="col" | DINO
! scope="col" | Nek5000
|-
| Connectivity
| Unstructured
| Structured
| Unstructured
|-
| Discretization Type
| Finite Volumes
| Finite Differences
| Spectral Elements
|-
| Grid point distribution
| Regular hexahedra
| Regular hexahedra
| Regular hexahedra with GLL points
|-
| Spatial order
| 4th
| 6th
| 7th - 15th (typically)
|-
| Temporal method
| expl. RK4
| expl. RK4 / semi-impl. RK3
| semi-impl. BDF3
|-
| Pressure solver
| CG with Deflation MPrec.
| FFT-based
| CG/GMRES with Jacobi/Schwartz Prec.
|-
| Thermo-chemistry
| Cantera (re-coded)
| Cantera
| Chemkin interface
|-
| Chemistry integration
| CVODE
| expl. RK4
| CVODE
|-
| Operator splitting
| Yes
| No
| No
|-
| Parallel paradigm
| MPI
| MPI
| MPI
|}

= References =

<references>
<ref name="moureau2011">
<bibtex>
@article{Moureau2011,
author= {V. Moureau, P. Domingo, and L. Vervisch},
title= {From large-eddy simulation to direct numerical simulation of a lean premixed swirl flame: Filtered laminar flame-pdf modeling},
journal={Combust. Flame},
year= {2011},
volume={158},
number={7},
pages={1340--1357},
}
</bibtex>
</ref>
<ref name="benard2015">
<bibtex>
@article{Benard2015,
author= {P. Benard, G. Balarac, V. Moureau, C. Dobrzynski, G. Lartigue, and Y. D’Angelo},
title= {Mesh adaptation for largeeddy simulations in complex geometries},
journal={Int. J. Numer. Methods Fluids},
year= {2015},
volume={81},
pages={719--740},
}
</bibtex>
</ref>
<ref name="chorin1968">
<bibtex>
@article{Chorin1968,
author= {A.J. Chorin},
title= {Numerical solution of the Navier-Stokes equations},
journal={Math. Computation},
year= {1968},
volume={22},
number={104},
pages={745--762},
}
</bibtex>
</ref>
<ref name="kraushaar2011">
<bibtex>
@article{Kraushaar2011,
author= {M. Kraushaar},
title= {Application of the compressible and low-Mach number approaches to Large-Eddy Simulation of turbulent flows in aero-engines},
journal={ PhD thesis, PhD, Institut National Polytechnique de Toulouse-INPT},
year= {2011},
}
</bibtex>
</ref>
<ref name="malandain2013">
<bibtex>
@article{Malandain2013,
author= {M. Malandain, N. Maheu, and V. Moureau},
title= {Optimization of the deflated conjugate gradient algorithm for the solving of elliptic equations on massively parallel machines},
journal={J. Comput. Phys.},
year= {2013},
volume={238},
pages={32--47},
}
</bibtex>
</ref>
<ref name="pierce2004">
<bibtex>
@article{Pierce2004,
author= {C.D. Pierce and P. Moin},
title= {Progress-variable approach for large-eddy simulation of non-premixed turbulent combustion},
journal={J. Fluid Mech.},
year= {2004},
volume={504},
pages={73--97},
}
</bibtex>
</ref>
<ref name="goodwin2003">
<bibtex>
@article{Goodwin2003,
author= {A.J. Chorin},
title= {An open-source, extensible software suite for CVD process simulation},
journal={Chemical Vapor Deposition XVI and EUROCVD},
year= {2003},
volume={14},
pages={2003--2008},
}
</bibtex>
</ref>
<ref name="hirschfelder1964">
<bibtex>
@article{Hirschfelder1964,
author= {J. Hirschfelder, R.B. Bird, and C.F. Curtiss},
title= {Molecular Theory of Gases and Liquids},
journal={Wiley},
year= {1964},
}
</bibtex>
</ref>
<ref name="sutherland1893">
<bibtex>
@article{Sutherland1893,
author= {W. Sutherland. LII},
title= {The viscosity of gases and molecular force},
journal={The London, Edinburgh, and Dublin Philosophical
Magazine and Journal of Science},
year= {1893},
volume={36},
number={223},
pages={507--531},
}
</bibtex>
</ref>
<ref name="cohen1996cvode">
<bibtex>
@article{Cohen1996cvode,
author= {S.D. Cohen, A.C. Hindmarsh, and P.F. Dubois},
title= {CVODE, a stiff/nonstiff ODE solver in C},
journal={Computers Phys.},
year= {1996},
volume={10},
number={2},
pages={138--143},
}
</bibtex>
</ref>
<ref name="sundials">
<bibtex>
@article{Sundials,
author= {A.C. Hindmarsh, P.N. Brown, K.E. Grant, S.L. Lee, R. Serban, D.E. Shumaker, and C.S. Woodward},
title= {SUNDIALS: Suite of nonlinear and differential/algebraic equation solvers},
journal={ACM Trans. Math. Soft. (TOMS)},
year= {2005},
volume={31},
number={3},
pages={363--396},
}
</bibtex>
</ref>
<ref name="li2010">
<bibtex>
@article{Li2010,
author= {N. Li and S. Laizet},
title= {2DECOMP&FFT - a highly scalable 2D decomposition library and FFT interface},
journal={Cray User’s Group 2010 conference, Edinburgh},
year= {2010},
}
</bibtex>
</ref>
<ref name="ern1995">
<bibtex>
@article{Ern1995,
author= {A. Ern and V. Giovangigli},
title= {Fast and accurate multicomponent transport property evaluation},
journal={J. Comput. Phys.},
year= {1995},
volume={120},
pages={105--116},
}
</bibtex>
</ref>
<ref name="abdelsamie2019">
<bibtex>
@article{Abdelsamie2019,
author= {A. Abdelsamie and D. Thévenin.},
title= { On the behavior of spray combustion in a turbulent spatially-evolving jet investigated by direct numerical simulation},
journal={Proc. Combust. Inst.},
year= {2019},
volume={37},
number={3},
pages={2493--2502},
}
</bibtex>
</ref>
<ref name="abdelsamie2020">
<bibtex>
@article{Abdelsamie2020,
author= {A. Abdelsamie and D. Thévenin},
title= {Nanoparticle behavior and formation in turbulent spray flames investigated by DNS},
journal={Direct and Large Eddy Simulation XII, ERCOFTAC Series},
year= {2020},
volume={27},
}
</bibtex>
</ref>
<ref name="chi2020">
<bibtex>
@article{Chi2020,
author= {C. Chi, A. Abdelsamie, and D. Thévenin},
title= {A directional ghost-cell immersed boundary method for incompressible flows},
journal={J. Comput. Phys.},
year= {2020},
volume={404},
pages={109122--109142},
}
</bibtex>
</ref>
<ref name="chi2018">
<bibtex>
@article{Chi2018,
author= {C. Chi, A. Abdelsamie, and D. Thévenin},
title= {Direct numerical simulations of hotspot-induced ignition in homogeneous hydrogen-air pre-mixtures and ignition spot tracking},
journal={Flow Turbul. Combust.},
year= {2018},
volume={101},
number={1},
pages={103--121},
}
</bibtex>
</ref>
<ref name="oster2018">
<bibtex>
@article{Oster2018,
author= {T. Oster, A. Abdelsamie, M. Motejat, T. Gerrits, C. Rössl, D. Thévenin, and H. Theisel},
title= {On-the-fly tracking of flame surfaces for the visual analysis of combustion processes},
journal={Comput. Graph. Forum},
year= {2018},
volume={37},
number={6},
pages={358--369},
}
</bibtex>
</ref>
<ref name="abdelsamie2019-2">
<bibtex>
@article{Abdelsamie2019-2,
author= {A. Abdelsamie and D. Thévenin},
title= {Impact of scalar dissipation rate on turbulent spray combustion investigated by DNS},
journal={Direct and Large-Eddy Simulation XI, ERCOFTAC Series},
year= {2019},
volume={25},
}
</bibtex>
</ref>
<ref name="tomboulides1997">
<bibtex>
@article{Tomboulides1997,
author= {A.G. Tomboulides, J.C.Y. Lee, and S.A. Orszag},
title= {Numerical simulation of low Mach number reactive flows},
journal={J. Sci. Comput.},
year= {1997},
volume={12},
pages={139--167},
}
</bibtex>
</ref>
<ref name="deville2002">
<bibtex>
@article{Deville2002,
author= {M.O. Deville, P.F. Fischer, and E.H. Mund},
title= {High-order Methods for Incompressible Fluid Flows},
journal={Cambridge University Press},
year= {2002},
}
</bibtex>
</ref>
<ref name="tanarro2020">
<bibtex>
@article{Tanarro2020,
author= {A. Tanarro, F. Mallor, N. Offermans, A. Peplinski, R. Vinuesa, and P. Schlatter},
title= {Enabling adaptive mesh refinement for spectral-element simulations of turbulence around wing sections},
journal={Flow Turbul. Combust},
year= {2020},
volume={105},
number={2},
pages={415--436},
}
</bibtex>
</ref>
<ref name="chemkin">
<bibtex>
@article{Chemkin,
author= {R.J. Kee, F.M. Rupley, and J.A. Miller},
title= {Chemkin-II: A Fortran chemical kinetics package for the analysis of gas-phase chemical kinetics},
journal={SAND-89-8009},
year= {1989},
}
</bibtex>
</ref>
<ref name="MS">
<bibtex>
@article{MS,
author= {M. Schmitt, C.E. Frouzakis, A.G. Tomboulides, Y.M. Wright, and K. Boulouchos},
title= {Direct numerical simulation of the effect of compression on the flow, temperature and composition under engine-like conditions},
journal={Proc. Combust. Inst.},
year= {2015},
volume={35},
pages={3069--3077},
}
</bibtex>
</ref>
<ref name="TCC">
<bibtex>
@article{TCC,
author= {G.K. Giannakopoulos, C.E. Frouzakis, P.F. Fischer, A.G. Tomboulides, and K. Boulouchos},
title= {LES of the gasexchange process inside an internal combustion engine using a high-order method},
journal={Flow Turbul. Combust.},
year= {2020},
volume={104},
pages={673--692},
}
</bibtex>
</ref>
<ref name="catalytic">
<bibtex>
@article{Catalytic,
author= {B.O. Arani, C.E. Frouzakis, J. Mantzaras, and K. Boulouchos},
title= {Three-dimensional direct numerical simulations of turbulent fuel-lean H2/air hetero-/homogeneous combustion over Pt with detailed chemistry},
journal={Proc. Combust. Inst.},
year= {2017},
volume={36},
number={3},
pages={4355--4363},
}
</bibtex>
</ref>
<ref name="abdelsamie2016">
<bibtex>
@article{Abdelsamie2016,
author= {B.O. Arani, C.E. Frouzakis, J. Mantzaras, and K. BoulouchosA. Abdelsamie, G. Fru, F. Dietzsch, G. Janiga, and D. Thévenin},
title= {Towards direct numerical simulations of lowMach number turbulent reacting and two-phase flows using immersed boundaries},
journal={Comput. Fluids},
year= {2016},
volume={131},
number={5},
pages={123--141},
}
</bibtex>
</ref>
</references>