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

被引：7
作者：
Lorenzo Pareschi
Giovanni Russo
机构：
[1] Department of Mathematics, University of Ferrara, Via Machiavelli 35, Ferrara
[2] Department of Mathematics and Computer Science, University of Catania, Via A.Doria 6, Catania
来源：
Journal of Scientific Computing | 2005年 / 25卷 / 1-2期
关键词：
65C20; 82D25; high order shock capturing schemes; hyperbolic systems with relaxation; Runge-Kutta methods; stiff systems;
D O I：
10.1007/BF02728986
中图分类号：
学科分类号：
摘要：
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. © 2005, Springer Science+Business Media, Inc.
引用
收藏
页码：129 / 155
页数：26
相关论文
共 36 条
[1]  
Arora M., Roe P.L., Issues and strategies for hyperbolic problems with stiff source terms, pp. 139-154, (1998)
[2]  
Ascher U., Petzold L., Computer Methods for Ordinary Differential Equations, and Differential Algebraic Equations, (1998)
[3]  
Ascher U., Ruuth S., Spiteri R.J., Implicit-explicit Runge-Kutta methods for time dependent partial differential equations, Appl. Numer. Math., 25, pp. 151-167, (1997)
[4]  
Ascher U., Ruuth S., Wetton B., Implicit-explicit methods for time dependent PDE’s, SIAM J. Numer. Anal., 32, pp. 797-823, (1995)
[5]  
Aw A., Rascle M., Resurrection of second order models of traffic flow?, SIAM. J. Appl. Math., 60, pp. 916-938, (2000)
[6]  
Aw A., Klar A., Materne T., Rascle M., Derivation of continuum traffic flow models from microscopic follow-the-leader models, SIAM J. Appl. Math., 63, pp. 259-278, (2002)
[7]  
Caflisch R.E., Jin S., Russo G., Uniformly accurate schemes for hyperbolic systems with relaxation, SIAM J. Numer. Anal., 34, pp. 246-281, (1997)
[8]  
Chen G.Q., Levermore D., Liu T.P., Hyperbolic conservations laws with stiff relaxation terms and entropy, Comm. Pure Appl. Math., 47, pp. 787-830, (1994)
[9]  
Dia B.O., Schatzman M., Commutateur de certains semi-groupes holomorphes et applications aux directions alternées, Math. Modelling Num. Anal., 30, pp. 343-383, (1996)
[10]  
Gottlieb S., Shu C.-W., Total variation diminishing Runge-Kutta schemes, Math. Comp., 67, pp. 73-85, (1998)
1234