Implicit-explicit Runge-Kutta schemes and applications to hyperbolic systems with relaxation. (English) Zbl 1203.65111
Summary: 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.
MSC:
| 65L06 | Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations |
| 65C20 | Probabilistic models, generic numerical methods in probability and statistics |
| 82D25 | Statistical mechanics of crystals |
| 35L65 | Hyperbolic conservation laws |
| 65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |
Keywords:
Runge-Kutta methods; hyperbolic systems with relaxation; stiff systems; high order shock capturing schemesSoftware:
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