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

Jose Miguel Mantas Ruiz; Lorenzo Pareschi; Jose Antonio Carrillo; Julio Ortega Lopera

doi:10.3233/jcm-2004-41-206

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

Jose Miguel Mantas Ruiz^*
, Lorenzo Pareschi
, Jose Antonio Carrillo
, Julio Ortega Lopera

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

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.

Original language	English
Pages (from-to)	33-41
Number of pages	9
Journal	Journal of Computational Methods in Sciences and Engineering
Volume	4
Issue number	1-2
DOIs	https://doi.org/10.3233/jcm-2004-41-206
Publication status	Published - Feb 2004

Keywords

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

ASJC Scopus subject areas

General Engineering
Computer Science Applications
Computational Mathematics

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10.3233/jcm-2004-41-206

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title = "Parallel integration of hydrodynamical approximations of the Boltzmann equation for rarefied gases on a cluster of computers",

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 = "boltzmann equation, burnett equations, implicit runge-kutta methods, Parallel numerical algorithms, parallel stiff ODE solvers, relaxation",

author = "\{Mantas Ruiz\}, \{Jose Miguel\} and Lorenzo Pareschi and Carrillo, \{Jose Antonio\} and Lopera, \{Julio Ortega\}",

note = "Publisher Copyright: {\textcopyright} 2004 IOS Press and the authors.",

year = "2004",

month = feb,

doi = "10.3233/jcm-2004-41-206",

language = "English",

volume = "4",

pages = "33--41",

journal = "Journal of Computational Methods in Sciences and Engineering",

issn = "1472-7978",

publisher = "Sage",

number = "1-2",

}

Parallel integration of hydrodynamical approximations of the Boltzmann equation for rarefied gases on a cluster of computers. / Mantas Ruiz, Jose Miguel; Pareschi, Lorenzo; Carrillo, Jose Antonio et al.
In: Journal of Computational Methods in Sciences and Engineering, Vol. 4, No. 1-2, 02.2004, p. 33-41.

Research output: Contribution to journal › Article › peer-review

TY - JOUR

T1 - Parallel integration of hydrodynamical approximations of the Boltzmann equation for rarefied gases on a cluster of computers

AU - Mantas Ruiz, Jose Miguel

AU - Pareschi, Lorenzo

AU - Carrillo, Jose Antonio

AU - Lopera, Julio Ortega

PY - 2004/2

Y1 - 2004/2

N2 - 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.

AB - 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.

KW - boltzmann equation

KW - burnett equations

KW - implicit runge-kutta methods

KW - Parallel numerical algorithms

KW - parallel stiff ODE solvers

KW - relaxation

UR - https://www.scopus.com/pages/publications/27144523289

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DO - 10.3233/jcm-2004-41-206

M3 - Article

AN - SCOPUS:27144523289

SN - 1472-7978

VL - 4

SP - 33

EP - 41

JO - Journal of Computational Methods in Sciences and Engineering

JF - Journal of Computational Methods in Sciences and Engineering

IS - 1-2

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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