Particles on Demand method: theoretical analysis, simplification techniques and model extensions

TL;DR

This paper provides a rigorous analysis and improvements to the Particles on Demand method, including efficiency strategies, model generalizations with tunable Prandtl number, and integration of semi-Lagrangian concepts, validated by high Mach flow simulations.

Contribution

It introduces theoretical insights, efficiency enhancements, and model extensions to the Particles on Demand method, broadening its applicability and performance.

Findings

The model achieves high accuracy and stability across diverse conditions.

Efficiency strategies reduce computational costs significantly.

The generalized model includes a tunable Prandtl number.

Abstract

The Particles on Demand method [B. Dorschner, F. B\"{o}sch and I. V. Karlin, {\it Phys. Rev. Lett.} {\bf 121}, 130602 (2018)] was recently formulated with a conservative finite volume discretization and validated against challenging benchmarks. In this work, we rigorously analyze the properties of the reference frame transformation and its implications on the accuracy of the model. Based on these considerations, we propose strategies to boost the efficiency of the scheme and to reduce the computational cost. Additionally, we generalize the model such that it includes a tunable Prandlt number via quasi-equilibrium relaxation. Finally, we adapt concepts from the multi-scale semi-Lagrangian lattice Boltzmann formulation to the proposed framework, further improving the potential and the operating range of the kinetic model. Numerical simulations of high Mach compressible flows demonstrate excellent accuracy and stability of the model over a wide range of conditions.