A positive finite-difference advection scheme
Journal of Computational Physics
Implicit-explicit Runge-Kutta methods for time-dependent partial differential equations
Applied Numerical Mathematics - Special issue on time integration
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
SIAM Journal on Scientific Computing
Multirate Timestepping Methods for Hyperbolic Conservation Laws
Journal of Scientific Computing
On adaptive mesh refinement for atmospheric pollution models
ICCS'05 Proceedings of the 5th international conference on Computational Science - Volume Part II
A multirate time integrator for regularized Stokeslets
Journal of Computational Physics
A self-organizing Lagrangian particle method for adaptive-resolution advection-diffusion simulations
Journal of Computational Physics
Numerical solution of multiscale problems in atmospheric modeling
Applied Numerical Mathematics
Extrapolated Multirate Methods for Differential Equations with Multiple Time Scales
Journal of Scientific Computing
Journal of Computational Physics
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Explicit time integration methods can be employed to simulate a broad spectrum of physical phenomena. The wide range of scales encountered lead to the problem that the fastest cell of the simulation dictates the global time step. Multirate time integration methods can be employed to alter the time step locally so that slower components take longer and fewer time steps, resulting in a moderate to substantial reduction of the computational cost, depending on the scenario to simulate [S. Osher, R. Sanders, Numerical approximations to nonlinear conservation laws with locally varying time and space grids, Math. Comput. 41 (1983) 321-336; H. Tang, G. Warnecke, A class of high resolution schemes for hyperbolic conservation laws and convection-diffusion equations with varying time and pace grids, SIAM J. Sci. Comput. 26 (4) (2005) 1415-1431; E. Constantinescu, A. Sandu, Multirate timestepping methods for hyperbolic conservation laws, SIAM J. Sci. Comput. 33 (3) (2007) 239-278]. In air pollution modeling the advection part is usually integrated explicitly in time, where the time step is constrained by a locally varying Courant-Friedrichs-Lewy (CFL) number. Multirate schemes are a useful tool to decouple different physical regions so that this constraint becomes a local instead of a global restriction. Therefore it is of major interest to apply multirate schemes to the advection equation. We introduce a generic recursive multirate Runge-Kutta scheme that can be easily adapted to an arbitrary number of refinement levels. It preserves the linear invariants of the system and is of third order accuracy when applied to certain explicit Runge-Kutta methods as base method.