Implicit-explicit Runge-Kutta schemes and applications to hyperbolic systems with relaxation
Numerical Analysis
2010-09-16 v1 Computational Physics
Fluid Dynamics
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 methods (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
Cite
@article{arxiv.1009.2757,
title = {Implicit-explicit Runge-Kutta schemes and applications to hyperbolic systems with relaxation},
author = {L. Pareschi and G. Russo},
journal= {arXiv preprint arXiv:1009.2757},
year = {2010}
}