Applicability of regularized particles-on-demand method to solve Riemann problem

Abstract

The lattice Boltzmann method (LBM) is a promising rapidly evolving simulation tool designed to capture the physics of the mesoscopic flow. But it is well known that the standard LBM is severely restricted to problems with low flow speed and small temperature range. The novel Particle-on-demand method (PonD) allows us to numerically solve the discrete Boltzmann equation for high Mach numbers. But the propagation step becomes more computationally intensive. A large part of the computational cost comes from matrix inversions during the rescaling of discrete distribution functions from one system of reference to another. We propose another method of discrete distribution function rescaling by applying regularization and moment conversion to avoid matrix inversions. This improvement shows drastic acceleration in calculations in comparison with standard PonD. Regularized PonD was applied to solve Riemann problems for a range of parameters. Results obtained by this improved method were compared to results received by the standard PonD and the standard LBM. The conservation of mass, momentum and energy of the new numerical method was studied. The necessary conditions for the stability of the solution were obtained.