The role of relaxation time on the stability of LBM

Palabos General
#1

Hi everyone,

Recently I am working on the simulation of fluid at high Reynolds number using LBM. As you known, instability of LBM simulation becomes a problem when the Reynolds number is very high. So this is normally what I did to stabilize the simulation:

  1. I find that the instability of the simulation may be related to the compressibility error;
  2. Once all the parameters (in physical units) are defined, I am able to reduce the value of “tau” (relaxation time) such that the maximum velocity in lattice units can be reduced. (based on the fact that the Reynolds number is given and the resolution is limited);
  3. As a result, I can get a small enough Mach number. At the same time, the time step is also reduced. Therefore, the simulation takes more steps and time.

Based on the simulations I have been working on, the way of stabilize the simulation by reducing the relaxation time seems working quite well. However, I also find on some resources that a value of relaxation time very close to 0.5 will cause the instability of LBM simulation.

I am really confused about this. I appreciate any help from all of you. Thank you very much!

Best regards,
Gengchao

#2

Hi Gengchao,

I faced a similar issue too. Input parameter settings seem to behave differently as Literature suggests. Following numerous testing, my implication is that the further away Relaxation Time from 0.5, the more unstable the code becomes, regardless of Prandtl number.

I am currently following a Paper regarding Entropy Balance as treatment to Dispersive Oscillations, which I believe is the cause of our instability issue.
ENHANCEMENT OF THE STABILITY OF LATTICE BOLTZMANN
METHODS BY DISSIPATION CONTROL
by ALEXANDER N. GORBAN AND DAVID J. PACKWOOD.
URL: https://www.ma.utexas.edu/mp_arc/c/13/13-20.pdf

Anyone who has succeeded in fitting this concept into D2Q9. Your sharing and insight will be greatly appreciated here.

Regards,
Victoria