Re: [ESPResSo-users] Multi-realaxation time model

[Wink, Markus]

Hello Ulf,

thanks a lot.

But I am still puzzled concerning the matrix. I thought that the collision 
operator  Omega should look something like that in MRT:
Omega = M^-1*S*(m_eq-m)

whereas M transforms the distribution function f into momentum space: m = M*f.
S is a diagonal matrix of the form = diag(s_0,s_1,....,s_18) consisting of the 
relaxation parameters. So basically in D3Q19 the matrix S should has 19 
parameters.
I assume that, for instance, s_0 should be equal to 1 (incompressible limit of 
the LBM ???) and that some are equal.

The question I have is: If there are four relaxation parameters in ESPResSo 
(`gamma_shear`, `gamma_bulk`, `gamma_odd`, `gamma_even`), how is the diagonal 
matrix S explicit built out of them?

Cheers,

Markus



-----Ursprüngliche Nachricht-----
Von: address@hidden [mailto:address@hidden Im Auftrag von Ulf Schiller
Gesendet: Dienstag, 30. Juni 2015 09:23
An: address@hidden
Betreff: Re: [ESPResSo-users] Multi-realaxation time model

On 30/06/15 08:16, Wink, Markus wrote:
> Dear ESPResSo users and developers,
> 
>  
> 
> I have a question concerning the MRT Lattice Boltzmann model used in 
> ESPResSo. In MRT the linearized collision operator is transformed to 
> momentum space via the collision matrix M. I have found the collision 
> matrix in the file lb-d3q19.hpp.
> 
> But I didn't find the relaxation parameters.
> 
>  
> 
> Shouldn't there be some kind of diagonal matrix S containing the 
> relaxation rates for the different moments?
> 
> Does anybody know where I can find them or tell me which relaxation 
> rates ESPResSo is using for the MRT algorithm?

The relaxation rates are `gamma_shear`, `gamma_bulk`, `gamma_odd`, `gamma_even` 
and are set in `lb_reinit_parameters()`.

Cheers,
Ulf

--
Dr Ulf D Schiller
Centre for Computational Science
University College London
20 Gordon Street
London WC1H 0AJ
United Kingdom

Phone: +44 (0)20 7679 5300