Particles on demand for flows with strong discontinuities

Particles-on-demand formulation of kinetic theory [B. Dorschner, F. Bösch and I. V. Karlin, Phys. Rev. Lett. 121, 130602 (2018), 10.1103/PhysRevLett.121.130602] is used to simulate a variety of compressible flows with strong discontinuities in density, pressure, and velocity. Two modifications are applied to the original formulation of the particles-on-demand method. First, a regularization by Grad's projection of particles populations is combined with the reference frame transformations in order to enhance stability and accuracy. Second, a finite-volume scheme is implemented which allows tight control of mass, momentum, and energy conservation. The proposed model is validated with an array of challenging one- and two-dimensional benchmarks of compressible flows, including hypersonic and near-vacuum situations, Richtmyer-Meshkov instability, double Mach reflection, and astrophysical jet. Excellent performance of the modified particles-on-demand method is demonstrated beyond the limitations of other lattice Boltzmann-like approaches to compressible flows.