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

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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

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Authors and Affiliations

  1. Department of Mathematics, University of Ferrara, Via Machiavelli 35, I-44100, Ferrara, Italy

    Lorenzo Pareschi

  2. Department of Mathematics and Computer Science, University of Catania, Via A.Doria 6, 95125, Catania, Italy

    Giovanni Russo

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  1. Lorenzo Pareschi
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  2. Giovanni Russo
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Correspondence to Lorenzo Pareschi.

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Pareschi, L., Russo, G. Implicit–Explicit Runge–Kutta Schemes and Applications to Hyperbolic Systems with Relaxation. J Sci Comput 25, 129–155 (2005). https://doi.org/10.1007/s10915-004-4636-4

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  • DOI: https://doi.org/10.1007/s10915-004-4636-4

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