Projective Integration Schemes for Hyperbolic Moment Equations

TL;DR

This paper demonstrates how projective integration schemes can efficiently solve hyperbolic moment equations related to the Boltzmann and BGK models, offering significant speedups while maintaining accuracy in multi-scale kinetic problems.

Contribution

It introduces the application of explicit, asymptotic-preserving projective integration methods to hyperbolic moment models, highlighting their effectiveness for multi-scale kinetic equations.

Findings

Spectral analysis reveals clear spectral gaps in linearized models.

Projective integration achieves significant computational speedup.

Method maintains accuracy across various test cases with different parameters.

Abstract

In this paper, we apply projective integration methods to hyperbolic moment models of the Boltzmann equation and the BGK equation, and investigate the numerical properties of the resulting scheme. Projective integration is an explicit, asymptotic-preserving scheme that is tailored to problems with large spectral gaps between slow and (one or many) fast eigenvalue clusters of the model. The spectral analysis of a linearized moment model clearly shows spectral gaps and reveals the multi-scale nature of the model for which projective integration is a matching choice. The combination of the non-intrusive projective integration method with moment models allows for accurate, but efficient simulations with significant speedup, as demonstrated using several 1D and 2D test cases with different collision terms, collision frequencies and relaxation times.