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

Published online by Cambridge University Press:  03 June 2015

Georgij Bispen*
Affiliation:
Institute of Mathematics, University of Mainz, Germany
K. R. Arun*
Affiliation:
School of Mathematics, Indian Institute of Science Education and Research Thiruvananthapuram, India
Mária Lukáčová-Medvid’ová*
Affiliation:
Institute of Mathematics, University of Mainz, Germany
Sebastian Noelle*
Affiliation:
IGPM, RWTH Aachen, Germany
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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.

Type
Research Article
Copyright
Copyright © Global Science Press Limited 2014

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