A positive finite-difference advection scheme
Journal of Computational Physics
Efficient implementation of weighted ENO schemes
Journal of Computational Physics
Implicit-explicit Runge-Kutta methods for computing atmospheric reactive flows
Applied Numerical Mathematics - Selected papers on eighth conference on the numerical treatment of differential equations 1-5 September 1997, Alexisbad, Germany
Multirate Timestepping Methods for Hyperbolic Conservation Laws
Journal of Scientific Computing
Linear Instability of the Fifth-Order WENO Method
SIAM Journal on Numerical Analysis
Multirate Runge-Kutta schemes for advection equations
Journal of Computational and Applied Mathematics
On adaptive mesh refinement for atmospheric pollution models
ICCS'05 Proceedings of the 5th international conference on Computational Science - Volume Part II
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Explicit time integration methods are characterized by a small numerical effort per time step. In the application to multiscale problems in atmospheric modeling, this benefit is often more than compensated by stability problems and stepsize restrictions resulting from stiff chemical reaction terms and from a locally varying Courant-Friedrichs-Lewy (CFL) condition for the advection terms. In the present paper, we address this problem by a rather general splitting technique that may be applied recursively. This technique allows the combination of implicit and explicit methods (IMEX splitting) as well as the local adaptation of the time stepsize to the meshwidth of non-uniform space grids in an explicit multirate discretization of the advection terms. Using a formal representation as partitioned Runge-Kutta method, convergence of order p=