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Implicit-Explicit Runge-Kutta schemes and applications to hyperbolic systems with relaxation (2000)
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| Venue: | Journal of Scientific Computing |
| Citations: | 82 - 14 self |
BibTeX
@ARTICLE{Pareschi00implicit-explicitrunge-kutta,
author = {Lorenzo Pareschi and Giovanni Russo},
title = {Implicit-Explicit Runge-Kutta schemes and applications to hyperbolic systems with relaxation},
journal = {Journal of Scientific Computing},
year = {2000},
volume = {3},
pages = {269--287}
}
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Abstract
We consider implicit-explicit (IMEX) Runge Kutta methods for hyperbolic systems of conservation laws with stiff relaxation terms. The explicit part is treated by a strong-stabilitypreserving (SSP) scheme, and the implicit part is treated by an L-stable diagonally implicit Runge Kutta (DIRK). The schemes proposed are asymptotic preserving (AP) in the zero relaxation limit. High accuracy in space is obtained by finite difference discretization with Weighted Essentially Non Oscillatory (WENO) reconstruction. After a brief description of the mathematical properties of the schemes, several applications will be presented. Keywords: Runge-Kutta methods, hyperbolic systems with relaxation, stiff systems, high order shock capturing schemes. AMS Subject Classification: 65C20, 82D25 1
Keyphrases
implicit-explicit runge-kutta scheme hyperbolic system runge kutta method explicit part high accuracy stiff system relaxation limit stiff relaxation term implicit runge kutta brief description am subject classification asymptotic preserving finite difference discretization conservation law implicit part mathematical property weighted essentially non oscillatory high order shock runge-kutta method several application
