Implementation of multirate time integration methods for air pollution modelling

摘要

Explicit time integration methods are characterised by a small numericaleffort per time step. In the application to multiscale problemsin atmospheric modelling, this benefit is often more than compensatedby stability problems and step size restrictions resulting from stiffchemical reaction terms and from a locally varyingCourant-Friedrichs-Lewy (CFL) condition for the advection terms.Splitting methods may be applied to efficiently combine implicit andexplicit methods (IMEX splitting). Complementarily multirate time integrationschemes allow for a local adaptation of the time step size to the grid size.In combination, these approaches lead to schemes which are efficientin terms of evaluations of the right-hand side. Special challenges arisewhen these methods are to be implemented. For an efficient implementation,it is crucial to locate and exploit redundancies. Furthermore, the morecomplex programme flow may lead to computational overhead which, in the worstcase, more than compensates the theoretical gain in efficiency.We present a general splitting approach which allows both for IMEX splittingsand for local time step adaptation. The main focus is on an efficientimplementation of this approach for parallel computation on computer clusters.