Abstract
Abstract. Explicit time integration methods are characterised by a small numerical effort per time step. In the application to multiscale problems in atmospheric modelling, this benefit is often more than compensated by stability problems and step size restrictions resulting from stiff chemical reaction terms and from a locally varying Courant-Friedrichs-Lewy (CFL) condition for the advection terms. Splitting methods may be applied to efficiently combine implicit and explicit methods (IMEX splitting). Complementarily multirate time integration schemes allow for a local adaptation of the time step size to the grid size. In combination, these approaches lead to schemes which are efficient in terms of evaluations of the right-hand side. Special challenges arise when these methods are to be implemented. For an efficient implementation, it is crucial to locate and exploit redundancies. Furthermore, the more complex programme flow may lead to computational overhead which, in the worst case, more than compensates the theoretical gain in efficiency. We present a general splitting approach which allows both for IMEX splittings and for local time step adaptation. The main focus is on an efficient implementation of this approach for parallel computation on computer clusters.
Highlights
Atmospheric processes can be described using advectiondiffusion-reaction equations
In the application to multiscale problems in atmospheric modelling, this benefit is often more than compensated by stability problems and step size restrictions resulting from stiff chemical reaction terms and from a locally varying Courant-FriedrichsLewy (CFL) condition for the advection terms
We present a general splitting approach which allows both for IMEX splittings and for local time step adaptation
Summary
The advection term describes transport due to wind, diffusion describes turbulent mixing on spatial scales below the cell size Both of these terms can efficiently be solved using explicit Runge-Kutta (RK) methods. Since the 1980s explicit multirate methods have been developed (e.g., Osher and Sanders, 1983; Tang and Warnecke, 2005) which allow for efficient solution of problems which can be split into nonstiff sub-systems with differing characteristic times, for example, advection on locally refined grids. The current paper is concerned with the efficient implementation of this scheme in the state-of-the-art Multiscale Atmospheric Chemistry and Transport model COSMO-MUSCAT (Wolke et al, 2004; Hinneburg et al, 2009) developed at the Institute for Tropospheric Research in Leipzig. We present two scenarios and discuss the obtained reduction of computational cost for each of them
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