Implementation of Asymptotic Preserving Discrete Velocity Methods into the Simulation Code PICLas

TL;DR

This paper introduces a second-order asymptotic preserving discrete velocity method for the BGK equation, maintaining positivity and enabling efficient multiscale gas flow simulations, with detailed implementation and performance evaluation.

Contribution

It presents a novel second-order asymptotic preserving discrete velocity method with positivity preservation, applicable to multiscale gas flow simulations, and details its deterministic implementation.

Findings

Method maintains positivity with cell-local distribution functions.

Performance evaluated successfully on multiple test cases.

Provides a robust toolbox for multiscale gas phenomena simulation.

Abstract

The Bhatnagar-Gross-Krook (BGK) model of the Boltzmann equation allows for efficient flow simulations, especially in the transition regime between continuum and high rarefaction. However, ensuring efficient performances for multiscale flows, in which the Knudsen number varies by several orders of magnitude, is never straightforward. Discrete velocity methods as well as particle-based solvers can each reveal advantageous in different conditions, but not without compromises in specific regimes. This article presents a second-order asymptotic preserving discrete velocity method to solve the BGK equation, with the particularity of maintaining positivity when operations are conducted with the cell-local distribution function. With this procedure based on exponential differencing, it is therefore also possible to construct an adapted version of this second-order method using the stochastic particle approach, as previously presented. The deterministic variant and its implementation are detailed here and its performances are evaluated on several test cases. Combined to the probabilistic solver and with the possibility of a future coupling, our exponential differencing discrete velocity method provides a robust toolbox, useful for efficiently simulating multiscale gas phenomena.