# D3Q15 vs D3Q19 vs D3Q27

Hi all,

I’ve poked through the literature some and these seem to be the three preferred methods for three dimentional cubic lattices. I was wondering if anybody could tell me the advantages/disadvantages of the three methods.

At the moment I’m using D3Q15 because it requries less work per iteration - however I am having difficulties with convergence at higher Reynolds numbers. Will more directions help? Do they reduce the number of interations to convergence? Why exactly would I want to use D3Q19 or D3Q27 over D3Q15?

Any hints?

Hi,
You can D3Q19 model. We know that number of Velocity direction increases accurate also will increase. But computational time, iterations, complexity of the code will increase. At higher Reynolds numbers D3Q19 and D3Q27 difference is not that much (Ref: li shi luo, JCP 2005).

Dear all,

Is the increase in lattice velocities only justified for stability/convergence reasons when computing high Reynolds number flows? Or are there any other advantages?

Thanks in advance for the help. To me the D3Q15 vs D3Q19 vs D3Q27 issue is still rather obscure therefore, if anyone knows some article(s) where this is discussed please post the references.

Regards

GoncaloSilva

Dear Goncalo,

if you want to simulate the energy equation (heat transfer etc.), D3Q15 or D3Q19 are not sufficient, since you cannot recover the equations in the macroscopic limit. You need more degrees of freedom and more velocities for that. I cannot tell you much more, but you should only use more than 19 velocities when you deal with the energy equation.
There is also a related thread somewhere around. The question was how to correctly recover higher velocity moments from the equilibrium distribution. In standard LBM, only the zeroth, first and second moments are correct. For the energy equation you also need higher moments, and thus at least third order in the equilibrium.

Best,
Timm

Dear Timm

Thank you for your answer. Yes, I know that in order to correctly reproduce higher order moments (which are related for instance with energy conservation) one needs to have more velocities in the LB model.
My question was more about the reason behind people using the D3Q19 model instead of the D3Q15. If both models reproduce equally well the hydrodynamic equations and the D3Q15 is not so computationally heavy as the D3Q19 why even bother to use this last. Is it just because of its larger stability?
If you or someone know the answer for that or some paper explaining the differences, i.e. advantages/disadvantages between these two LB model I would be very grateful if the reference is posted here.

Regards

Goncalo

I am only aware of stability and accuracy advantages of D3Q19 over D3Q15. In other words: If you have heavy simulations, and you are not interested in optimum accuracy and you are using a relaxation parameter well above 0.5, you should use D3Q15 to save time.

Timm

Hi everyone,

Thank you

Daralcan

Dear Daralcan

As far as I am aware there are not much published studies on that subject.
One of the few articles that I know providing some discussion on the comparision among different 3D lattices is the following: