Particles on Demand for flows with strong discontinuities

TL;DR

This paper enhances the Particles on Demand kinetic theory method to accurately simulate complex compressible flows with discontinuities, using regularization and finite-volume schemes for improved stability and conservation.

Contribution

The paper introduces modifications to the Particles on Demand method, combining regularization and finite-volume schemes to improve stability, accuracy, and conservation in simulating strong discontinuities in compressible flows.

Findings

Successfully simulates hypersonic and near-vacuum flows.

Accurately captures Richtmyer-Meshkov instability and double Mach reflection.

Demonstrates superior performance over other lattice Boltzmann methods.

Abstract

Particles on Demand formulation of kinetic theory [B. Dorschner, F. B\"{o}sch and I. V. Karlin, {\it Phys. Rev. Lett.} {\bf 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.