Implicit-explicit runge-kutta schemes and applications to hyperbolic systems with relaxation

Lorenzo Pareschi; Giovanni Russo

doi:10.1007/BF02728986

Implicit-explicit runge-kutta schemes and applications to hyperbolic systems with relaxation

Lorenzo Pareschi
, Giovanni Russo

University of Ferrara
Università di Catania

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

31 Scopus citations

Abstract

We consider new implicit-explicit (IMEX) Runge-Kutta methods for hyperbolic systems of conservation laws with stiff relaxation terms. The explicit part is treated by a strong-stability-preserving (SSP) scheme, and the implicit part is treated by an L-stable diagonally implicit Runge-Kutta method (DIRK). The schemes proposed are asymptotic preserving (AP) in the zero relaxation limit. High accuracy in space is obtained by Weighted Essentially Non Oscillatory (WENO) reconstruction. After a description of the mathematical properties of the schemes, several applications will be presented.

Original language	English
Pages (from-to)	129-155
Number of pages	27
Journal	Journal of Scientific Computing
Volume	25
Issue number	1-2
DOIs	https://doi.org/10.1007/BF02728986
State	Published - Nov 2005
Externally published	Yes

Keywords

65C20
82D25
Runge-Kutta methods
high order shock capturing schemes
hyperbolic systems with relaxation
stiff systems

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10.1007/BF02728986

Cite this

@article{348b046681fc491f885221ee0c8ca56a,

title = "Implicit-explicit runge-kutta schemes and applications to hyperbolic systems with relaxation",

abstract = "We consider new implicit-explicit (IMEX) Runge-Kutta methods for hyperbolic systems of conservation laws with stiff relaxation terms. The explicit part is treated by a strong-stability-preserving (SSP) scheme, and the implicit part is treated by an L-stable diagonally implicit Runge-Kutta method (DIRK). The schemes proposed are asymptotic preserving (AP) in the zero relaxation limit. High accuracy in space is obtained by Weighted Essentially Non Oscillatory (WENO) reconstruction. After a description of the mathematical properties of the schemes, several applications will be presented.",

keywords = "65C20, 82D25, Runge-Kutta methods, high order shock capturing schemes, hyperbolic systems with relaxation, stiff systems",

author = "Lorenzo Pareschi and Giovanni Russo",

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T1 - Implicit-explicit runge-kutta schemes and applications to hyperbolic systems with relaxation

AU - Pareschi, Lorenzo

AU - Russo, Giovanni

PY - 2005/11

Y1 - 2005/11

N2 - We consider new implicit-explicit (IMEX) Runge-Kutta methods for hyperbolic systems of conservation laws with stiff relaxation terms. The explicit part is treated by a strong-stability-preserving (SSP) scheme, and the implicit part is treated by an L-stable diagonally implicit Runge-Kutta method (DIRK). The schemes proposed are asymptotic preserving (AP) in the zero relaxation limit. High accuracy in space is obtained by Weighted Essentially Non Oscillatory (WENO) reconstruction. After a description of the mathematical properties of the schemes, several applications will be presented.

AB - We consider new implicit-explicit (IMEX) Runge-Kutta methods for hyperbolic systems of conservation laws with stiff relaxation terms. The explicit part is treated by a strong-stability-preserving (SSP) scheme, and the implicit part is treated by an L-stable diagonally implicit Runge-Kutta method (DIRK). The schemes proposed are asymptotic preserving (AP) in the zero relaxation limit. High accuracy in space is obtained by Weighted Essentially Non Oscillatory (WENO) reconstruction. After a description of the mathematical properties of the schemes, several applications will be presented.

KW - 65C20

KW - 82D25

KW - Runge-Kutta methods

KW - high order shock capturing schemes

KW - hyperbolic systems with relaxation

KW - stiff systems

UR - https://www.scopus.com/pages/publications/85097576287

U2 - 10.1007/BF02728986

DO - 10.1007/BF02728986

M3 - Article

AN - SCOPUS:85097576287

SN - 0885-7474

VL - 25

SP - 129

EP - 155

JO - Journal of Scientific Computing

JF - Journal of Scientific Computing

IS - 1-2

ER -

Implicit-explicit runge-kutta schemes and applications to hyperbolic systems with relaxation

Abstract

Keywords

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