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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
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