Communications in Mathematical Sciences

Volume 14 (2016)

Number 2

High order semi-Lagrangian methods for the BGK equation

Pages: 389 – 414

DOI: http://dx.doi.org/10.4310/CMS.2016.v14.n2.a4

Authors

Maria Groppi (Department of Mathematics and Computer Science, University of Parma, Italy)

Giovanni Russo (Department of Mathematics and Computer Science, University of Catania, Italy)

Giuseppe Stracquadanio (Department of Mathematics and Computer Science, University of Parma, Italy)

Abstract

A new class of high-order accuracy numerical methods for the BGK model of the Boltzmann equation is presented. The schemes are based on a semi-Lagrangian formulation of the BGK equation; time integration is dealt with DIRK (Diagonally Implicit Runge–Kutta) and BDF methods; the latter turn out to be accurate and computationally less expensive than the former. Numerical results and examples show that the schemes are reliable and efficient for the investigation of both rarefied and fluid regimes in gas dynamics.

Keywords

Boltzmann equation, BGK equation, semi-Lagrangian methods, high-order schemes

2010 Mathematics Subject Classification

65L06, 65M25, 76P05

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Published 14 December 2015