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


From: Ulf Schiller
Subject: Re: [ESPResSo-users] Multi-realaxation time model
Date: Tue, 30 Jun 2015 09:23:10 +0100
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On 30/06/15 09:10, Wink, Markus wrote:
> 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?

The application of the matrix S is performed in `lb_relax_modes(...)`
where you can read off how the relaxation parameters relate to the
matrix. Due to symmetries there are only four relaxation parameters, and
often only gamma_odd and gamma_even are used (TRT - two relaxation time
model).

Cheers,
Ulf

> -----Urspr√ľngliche 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



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