As far we know, the relaxation time for momentum equation tau_v > 0.50, and we choose it in such a way that it satisfies the relation: 0 < omega < 2.0, where omega=1/tau_v . Now I would like to know, is there any limitation of relaxation time for energy equation (tau_t) like momentum equation? With all the best
as for the N-S equation there are limitations. As pointed out tau > 1/2 is a necessary to be physically consistent. But one has to pay attention to the fact that there should also be an upper limit. When one does the Chapman-Enskog expansion of a lattice boltzmann model to recover the macroscopic equation he wants to simulate, the f’s are expanded in terms of a small parameter, usually noted “epsilon”, which is usually interpreted as the Knudsen number. The Knudsen number is the mean free path over the characteristic length of the physical setup. The Knudsen number is of course related to the relaxation time of you model. Therefore one has to be careful when dealing with too big relaxation times.
Furthermore, the range of acceptable relaxation times is related to a lot of parameters. The collision you are using, but also the boundary conditions (this is the most important in my opinion), the geometry of the problem, the spatial and time resolution of the problem, … Therefore, it is really difficult to give a general constrain on the relaxation time apart from the nu>0 and Knudsen <<1.