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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Official URL: http://www.springerlink.com/content/25g707347w53p2...

## Abstract

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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