*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 |

Radius | 0.005m |

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) / pi*180. = 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 |