Photo Chris Liverani

### Context of these academical Benchmarks

SCALABLE must “achieve the scaling to unprecedented performance, scalability, and energy efficiency of an industrial LBM-based computational fluid dynamics (CFD) software.” The following two benchmarks highlights the numerical precision with an academical convection of a vortex, and the turbulence modeling capacity with academical turbulent channels.

Both these benchmarks divided between a principal target, allowing a thorough validation of the property, and a secondary target, pushing the simulation to a more demanding situation.

### On convection accuracy

The first test case is the CERFACS CO-VO, already performed on many codes.

##### Definition

An isentropic vortex is simply moving to the east of a periodic square grid. With time. The flow is supposed inviscid Euler Equations

CO-VO Parameters
Density 1.1608 Kg/m3
Temperature 300 Kelvins
Pressure 10^5 Pascals
Circulation 34.728
Convection speed Uc = 170m/s (Mach 0.5)
Resolution 64x64
Domain -0.05, 0.05 m

You can download a Cerfacs Technical report giving more details on the initialization equations here.

Vortex convected by LEOPARD, a LBM testbed from cerfacs, 10th turnaround.

##### Secondary test: unaligned convection.

In LBM, the streaming operator is aligned with the grid. Therefore a vortex convection from west to east is a very good situation : only one direction is really working.

The secondary test is simply a convection with an angle, exactly atan(1/10) / pi180. = 5,71059314 degree*. Therefore, after 10 revolution, the vortex should still be in the center. The only difference is a small velocity component to the Y direction (south to north).

Unaligned CO-VO
Convection speed x Uc = 170m/s (Mach 0.5)
Convection speed y Vc = 17m/s

### On turbulence modeling

Turbulence modeling must be carefully assessed, starting with cases where the analytical theory allows to be quantitative. The first test case is a turbulent channel.

Streamwise velocity (sides) and wall-shear stress (top) of turbulent flow between two parallel plates SC13 Research Highlight: Petascale DNS of Turbulent Channel Flow

##### Turbulent flow between two parallel plates, Reynolds=10 000

The first turbulent channel is defined in the POF article of Moser: Robert D. Moser, John Kim, and Nagi N. Mansour. “Direct numerical simulation of turbulent channel flow up to Reτ = 590”. In: Physics of Fluids 11.4 (1999), pp. 943–945. doi: 10.1063/1.869966. url: https://doi.org/10.1063/1.869966.

Coarse mesh - regular
Shape LxHxW πH/2 x H x 0.289πH/2
Dimensions LxHxW 0,314 x 0,2 x 0,09 m
Resolution Dx 0,001m
Cells 5,652 Millions (1314x200x90)
Turbulent flow between two parallel plates
Domain Height 0.2
Density 1.1608 Kg/m3
Temperature 300 Kelvins
Pressure 10^5 Pascals
Bulk Reynolds 10 000
Bulk Velocity 1,61268091 m/s
Skin Friction coef. 5.908e-3
Tau wall 8,92E-03
Forcing term 0,089179448 kg/m2/s2
friction Reynolds 5,44E+02
Resolution 200
DeltaY 0,001
DeltaY+ 5,44E+00
##### Turbulent atmospheric boundary layer - Reynolds > 300 000 000

This second test comes from Large eddy simulation study of fully developed wind-turbine array boundary layers Physics of Fluids 22, 015110 (2010); https://doi.org/10.1063/1.3291077 Marc Calaf, Charles Meneveau, and Johan Meyers

Coarse mesh - regular
Shape LxHxW 11H x H x 0.31H
Resolution Dx 10m
Cells 34.1 Millions (1100 x 100 x 310)
Atmospheric boundary layer
Domain Height 1000m
Density 1.1608 Kg/m3
Temperature 300 Kelvins
Pressure 10^5 Pascals
Bulk Reynolds 3,63E+08
Bulk Velocity 5,85 m/s
Skin Friction coef. 1,25E-02
Tau wall 2,48E-01
Forcing term 0,000248284 kg/m2/s2
friction Reynolds 2,87E+07
DeltaY 10m
DeltaY+ 28677,91

Antoine Dauptain is a research scientist focused on computer science and engineering topics for HPC.