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IMEX Large Time Step Finite Volume Methods for Low Froude Number Shallow Water Flows

IMEX Large Time Step Finite Volume Methods for Low Froude Number Shallow Water Flows
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Year:    2014

Communications in Computational Physics, Vol. 16 (2014), Iss. 2 : pp. 307–347

Abstract

We present new large time step methods for the shallow water flows in the low Froude number limit. In order to take into account multiscale phenomena that typically appear in geophysical flows nonlinear fluxes are split into a linear part governing the gravitational waves and the nonlinear advection. We propose to approximate fast linear waves implicitly in time and in space by means of a genuinely multidimensional evolution operator. On the other hand, we approximate nonlinear advection part explicitly in time and in space by means of the method of characteristics or some standard numerical flux function. Time integration is realized by the implicit-explicit (IMEX) method. We apply the IMEX Euler scheme, two step Runge Kutta Cranck Nicolson scheme, as well as the semi-implicit BDF scheme and prove their asymptotic preserving property in the low Froude number limit. Numerical experiments demonstrate stability, accuracy and robustness of these new large time step finite volume schemes with respect to small Froude number.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.040413.160114a

Communications in Computational Physics, Vol. 16 (2014), Iss. 2 : pp. 307–347

Published online:    2014-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    41

Keywords:    Low Froude number flows

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