Implicit---Explicit Runge---Kutta Schemes and Applications to Hyperbolic Systems with Relaxation

Authors:
Lorenzo Pareschi;Giovanni Russo
Affiliations:
Department of Mathematics, University of Ferrara, Ferrara, Italy I-44100;Department of Mathematics and Computer Science, University of Catania, Catania, Italy 95125
Venue:
Journal of Scientific Computing
Year:
2005

Citing 18
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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