Simulation of two-dimensional decaying turbulence using the “incompressible” extensions of the lattice Boltzmann method

Incompressible extensions of the lattice Boltzmann method [Zou Q, Hou S, Chen S, Doolen GD. J Stat Phys 1995;81:35, He X, Luo LS. J Stat Phys 1997;88:927, Fang HP, Wan RZ, Lin ZF. Phys Rev E 2002;66:036314] are studied simulating two-dimensional decaying turbulence in a double-periodic domain. The simulation results are compared with reference calculations obtained by a pseudo-spectral code. It is shown that the standard method can perform better than the incompressible extensions even in the case of finite Mach number flows as long as density variations (pressure effects) are not significant in the domain. The importance of initializing not only the initial values of macroscopic variables but also the non-equilibrium part of the distribution functions is emphasized, and deviations arising from underspecified initial conditions are shown.