Implicit-explicit Runge-Kutta schemes and applications to hyperbolic systems with relaxation
This work provides numerical methods for efficiently solving hyperbolic systems with stiff relaxation, relevant to computational fluid dynamics and related fields.
The paper develops new IMEX Runge-Kutta schemes for hyperbolic systems with stiff relaxation, achieving asymptotic preservation in the zero relaxation limit and high spatial accuracy via WENO reconstruction. Numerical applications demonstrate the schemes' effectiveness.
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.