Calculation of Omega and Tau in converters

[bujji]

Dear OpenLB team,

I’m having a little confusion in the Converter. I’ve considered the example bstep2d. In that example, the paramters for the simulation setup of the domain has been given as follows:

Code:

Parameters for the simulation setup
const T lx1 = 5.0; // length of step in meter
const T ly1 = 0.75; // height of step in meter
const T lx0 = 20.0; // length of channel in meter
const T ly0 = 1.5; // height of channel in meter
const int N = 60; // resolution of the model
const int M = 50; // resolution of the model
const T maxPhysT = 40.; // max. simulation time in s, SI unit

if I’m correct, these are the physical units of the domain. By using Converter the physical units are converted into LB units as follows:

Code:

UnitConverter<T,DESCRIPTOR> converter(
(T) 1./N, // physDeltaX: spacing between two lattice cells in __m__
(T) 1./(M*N), // physDeltaT: time step in __s__
(T) 1., // charPhysLength: reference length of simulation geometry
(T) 1., // charPhysVelocity: maximal/highest expected velocity during simulation in __m / s__
(T) 1./500., //physViscosity: physical kinematic viscosity in m^2 / s
(T) 1. // physDensity: physical density in __kg / m^3__
);

Can you please explain the relation between physViscosity and Char Nu, physDensity and Char rho.?
Omega and Tau can be varied by Char Nu and Char L. can you please provide me any reference that can explain these relations.

thanks in advance.

[mgaedtke]

Hello bujji,

I suggest you to read chapter 7 in the book of Krügel et al. https://www.springer.com/de/book/9783319446479. You should find anwsers to your questions there, as we implented the converter class according to this chapter.

Best regards, Max

[bujji]

Hi Max,
Thanks for the references

[Author]

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