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
N1 - Publisher Copyright:
© 2004 IOS Press and the authors.
PY - 2004
Y1 - 2004
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 - Parallel numerical algorithms
KW - boltzmann equation
KW - burnett equations
KW - implicit runge-kutta methods
KW - parallel stiff ODE solvers
KW - relaxation
UR - http://www.scopus.com/inward/record.url?scp=27144523289&partnerID=8YFLogxK
U2 - 10.3233/jcm-2004-41-206
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 -