On the conservativity of the Particles-on-Demand method for solution of the Discrete Boltzmann Equation

It is well known that the standard Lattice-Boltzmann method (LBM) is applicable in the range of small flow velocities and under the isothermal conditions. The novel Particle-on-demand method [1] allows to numerically solve the discrete Boltzmann equation for high Mach numbers. We validate its capabilities with our implementation on the problems with shock waves. In comparison with the standard Lattice Boltzmann Method, the collision step is simple, but the streaming step is implicit, non-conservative and excessively computationally heavy. We propose a way that in specific cases improves the method by making the streaming step explicit and conservative. The results are validated by examining the total mass, momentum and energy change in the problem of shock formation due to the sound wave distortion. The scheme also performs well in both 1D and 3D test Sod problems.