Regularization and the particles-on-demand method for the solution of the discrete Boltzmann equation

In its classical formulation, the lattice Boltzmann method (LBM) is applicable in the range of subsonic velocities and small temperature ratios. The novel Particle-on-demand method (PonD) allows to numerically solve the discrete Boltzmann equation for high Mach numbers. In comparison with the standard LBM, the collision step is simple, but the streaming step is implicit, not mass conserving and computationally heavy. A large part of the computational cost comes from matrix inversions during the rescaling of the discrete distribution functions (DF) from one gauge to another. To avoid matrix inversions, we propose another method of discrete DF rescaling, where the discrete DF are restored from the moments, while the conversion to a different reference frame is in the moment space. Results obtained by this improved method were compared to results, received by standard PonD for a number of problems. This improvement is validated to produce similar results to the original PonD, and is computationally cheaper in comparison with PonD.