Parallel integration of hydrodynamical approximations of the Boltzmann equation for rarefied gases on a cluster of computers

Issue title: Computational and Mathematical Methods for Science and Engineering Conference 2002 – CMMSE-2002

Article type: Research Article

Authors: Mantas Ruiz, José Miguel^{a; *} | Pareschi, Lorenzo^b | Carrillo, José Antonio^c | Lopera, Julio Ortega^d

Affiliations: [a] Software Engineering Department. University of Granada C/P. Daniel de Saucedo s/n. 18071 Granada, Spain | [b] Department of Mathematics. University of Ferrara Via Machiavelli 35, I-44100 Italy | [c] ICREA, Depto. Matemàtiques, University Autònoma Barcelona, Bellaterra E-08193, Spain | [d] Computer Architecture and Technology Department. University of Granada C/P. Daniel de Saucedo s/n, 18071 Granada, Spain

Correspondence: [*] Corresponding author. Tel.: +34 958 243176; Fax: +34 958 243179; E-mail: jmmantas@ugr.es

Abstract: The relaxed Burnett system, recently introduced in as a hydrodynamical approximation of the Boltzmann equation, is numerically solved. Due to the stiffness of this system and the severe CFL condition for large Mach numbers, a fully implicit Runge-Kutta method has been used. In order to reduce computing time, we apply a parallel stiff ODE solver based on 4-stage Radau IIA IRK. The ODE solver is combined with suitable first order upwind and second order MUSCL relaxation schemes for the spatial derivatives. Speedup results and comparisons to DSMC and Navier-Stokes approximations are reported for a 1D shock profile.

Keywords: parallel numerical algorithms, boltzmann equation, burnett equations, parallel stiff ODE solvers, relaxation, implicit runge-kutta methods

DOI: 10.3233/JCM-2004-41-206

Journal: Journal of Computational Methods in Sciences and Engineering, vol. 4, no. 1-2, pp. 33-41, 2004