Communications in Mathematical Sciences

Volume 20 (2022)

Number 2

Some preliminary results on a high order asymptotic preserving computationally explicit kinetic scheme

Pages: 297 – 326

DOI: https://dx.doi.org/10.4310/CMS.2022.v20.n2.a1

Authors

Rémi Abgrall (Institute of Mathematics and Institute of Computational Sciences, Universität Zürich, Switzerland)

Davide Torlo (Inria Bordeaux-Sud-Ouest, Talence, France)

Abstract

In this short paper, we intend to describe one way to construct arbitrarily high order kinetic schemes on regular meshes. The method can be arbitrarily high order in space and time, run at least CFL one, is asymptotic preserving and computationally explicit, i.e., the computational costs are of the same order of a fully explicit scheme. We also introduce a nonlinear stability method that enables to simulate problems with discontinuities, and it does not kill the accuracy for smooth regular solutions.

Keywords

kinetic scheme, asymptotic preserving, high order, stability analysis

2010 Mathematics Subject Classification

65L04, 65M12, 65M60

Received 28 May 2019

Accepted 30 June 2021

Published 28 January 2022