Repository: Freie Universit├Ąt Berlin, Math Department

Multirate infinitesimal step methods for atmospheric flow simulation

Wensch, J. and Knoth, O. and Galant, A. (2009) Multirate infinitesimal step methods for atmospheric flow simulation. BIT - Numerical Mathematics, 49 (2). pp. 449-473. ISSN 0006-3835 (Print) 1572-9125 (Online)

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The numerical solution of the Euler equations requires the treatment of processes in different temporal scales. Sound waves propagate fast compared to advective processes. Based on a spatial discretisation on staggered grids, a multirate time integration procedure is presented here generalising split-explicit Runge-Kutta methods. The advective terms are integrated by a Runge-Kutta method with a macro stepsize restricted by the CFL number. Sound wave terms are treated by small time steps respecting the CFL restriction dictated by the speed of sound. Split-explicit Runge-Kutta methods are generalised by the inclusion of fixed tendencies of previous stages. The stability barrier for the acoustics equation is relaxed by a factor of two. Asymptotic order conditions for the low Mach case are given. The relation to commutator-free exponential integrators is discussed. Stability is analysed for the linear acoustic equation. Numerical tests are executed for the linear acoustics and the nonlinear Euler equations.

Item Type:Article
Uncontrolled Keywords:Runge Kutta methods - Multirate methods - Finite volume methods - Atmospheric dynamics
Subjects:Mathematical and Computer Sciences > Mathematics > Applied Mathematics
ID Code:734
Deposited By: Ulrike Eickers
Deposited On:12 Aug 2009 09:02
Last Modified:23 Aug 2009 08:57

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