In order to speed up my 3D LB computations I am thinking to change my LB code from the D3Q19 to the D3Q13 model. Based on some literature research I found that besides incorporating less particle velocities, the special arrangement of this lattice scheme allows one to reduce the number of nodes to half. So at first glance this change in LB models appears to be a very good deal.
However, I wonder why there aren’t many LB works using the D3Q13 model? I understand that I should not expect my numerical results to be as accurate as if I was using a LB model with more velocities. Nevertheless, to me the use of this model seems to pay off. Does anyone has any experience/opinion on this?
Any comments will be highly appreciated.
D3Q13 exists only in MRT formulation and this is one of the reason why people not to pursue it. You need to prepare all the boundary conditions according to MRT formulation if you want to get advantage out of it.
Overall, I think it’s a nice model but I’ve never used and can’t comment it thoroughly.
Regarding the point that the BCs should be prepared according to the MRT formulation… Could you, please expand a bit on this by pointing a suitable refference where this is explained? None of the articles I have read about MRT comment on having to prepare the BCs in a way that is different from the one for BGK for example.
Any comment, greatly appreciated.
D3Q13 exists only in MRT formulation and this is
one of the reason why people not to pursue it. You
need to prepare all the boundary conditions
according to MRT formulation if you want to get
advantage out of it.
Overall, I think it’s a nice model but I’ve never
used and can’t comment it thoroughly.
In fact I also did not understand Alex’s statement.
As far as I know BCs are traditionally implemented in velocity space. Examples of such BCs that take place in velocity space even when the MRT collision model is used are: bounceback (and its interpolation extensions), Zou-He (no-equilibrium bounceback), extrapolation (to the whole distribution function or just the non-equilibrium part), etc…
Nevertheless, it is true that the choice of the relaxation values of some ghost modes in the collision process may have some impact in the performance of the BC method and so yield more accurate results.
The reason why Alex said that D3Q13 needs to use MRT is because if only one relaxation time is used the viscosity parameter becomes anisotropic,
It’s my mistake about boundary conditions. I’ve heard about the preparation from somebody else, but then I tried to search in the literature right now I haven’t succeed. I guess it should come for the extrapolation methods but I can’t find.
The MRT formulation exists because of the viscosities anisotropy. In other words you need to have some ghost moments to restore the proper Navier-Stokes equation.
Once again I’ve never worked with it,
Sorry for the mistake,