Particles on Demand for flows with strong discontinuities

Abstract

Particles on Demand formulation of kinetic theory [B. Dorschner, F. Bösch 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.

Detonation modeling with the Particles on Demand method

“…The hydrodynamics is solved by the Particles on Demand (PonD) method [33][34][35]38]. The LBM models the flow in a constant global thermodynamic reference frame λ (u = 0, T = T L ).…”

“…The population is then transformed to be expressed in destination reference frame followed by collision. Details of the semi-Lagrangian propagation [33] and the transformation procedure [38] will be explained in section (III B) on propagation.…”