Particles on demand for flows with strong discontinuities

Particles-on-demand formulation of kinetic theory [B. Dorschner, F. B??sch and I. V. Karlin, Phys. Rev. Lett. 121, 130602 (2018)] 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.

Automated summary

The study utilizes the particles-on-demand method to simulate compressible flows with strong discontinuities in density, pressure, and velocity. The method is modified through regularization by Grad's projection and reference frame transformations, as well as the implementation of a finite-volume scheme to improve stability, accuracy, and conservation of mass, momentum, and energy. The proposed model demonstrates excellent performance in various benchmarks, surpassing the limitations of other lattice Boltzmann-like approaches to compressible flows.