Dear LB members;
I recently started using MRT-model for fluid flow and mass transport in porous media at pore and macroscopic scale.
I am trying to implement D2Q9-MRT-based anisotropic-advection dispersion (AADE) model for mass transport as proposed by Ginzburg (2005, Adv. WR).
I am linking MRT-based flow model (parameters used from Lallemand and Luo, 2000, PRE) with above-mentioned AADE- model. The AADE model works fine as long as relaxation parameters (s1(4,6)) remain less than 1.96 for any flow rate.
I need help to find better set of relaxation parameters (s1) to simulate low-diffusion problem
( (s1(4,6)~1.999) at high flow rate (~0.1 lu/ts).
I can send out my code written in MATLAB for debugging purposes. Following are parameters value I am using.
relaxation parameters:
s1=[0,-1.8,-1.2,-1.96,-1.5,-1.96,-1.5,-1.3,-1.3];
s1(4,6) controls the mass diffusion or Peclet number.
a21=-2;a31=1;c11=0;axx=0;axy= 0;
Following are moments
m_eq1(1) = rho1(j,i); %density
m_eq1(2) = (a21)rho1(j,i); %energy
m_eq1(3) = (a31)rho1(j,i); %energy square
m_eq1(4) = jxrho1(j,i); %momentum in x-dir
m_eq1(5) = (1/2)c11jx; %energy flux in x-dir
m_eq1(6) = jyrho1(j,i); %momentum in y-dir
m_eq1(7) = (1/2)c11jy; %energy flux in y-dir
m_eq1(8) = axxrho1(j,i); %diagonal comp of stress tensor
m_eq1(9) = axyrho1(j,i); %off diagonal comp of stress tensor
microscopic velocities:
e(1,:)=[1,0,-1,0,1,-1,-1,1,0]; %ex
e(2,:)=[0,1,0,-1,1,1,-1,-1,0]; %ey
weights:
wa(9)=4/9;wa(1:4)=1/9;wa(5:8)=1/36;%weights
M-matrix
M=[ 1,1,1,1,1,1,1,1,1;
-1,-1,-1,-1,2,2,2,2,-4;
-2,-2,-2,-2,1,1,1,1,4;
1,0,-1,0,1,-1,-1,1,0;
-2,0,2,0,1,-1,-1,1,0;
0,1,0,-1,1,1,-1,-1,0;
0,-2,0,2,1,1,-1,-1,0;
1,-1,1,-1,0,0,0,0,0;
0,0,0,0,1,-1,1,-1,0;
];
Thanks for help and suggestions.
Shadab.