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Finite volume and pseudo-spectral schemes for the fully nonlinear 1D Serre equations

Published online by Cambridge University Press:  24 May 2013

DENYS DUTYKH ,
DIDIER CLAMOND ,
PAUL MILEWSKI  and
DIMITRIOS MITSOTAKIS
DENYS DUTYKH
Affiliation:
School of Mathematical Sciences, University College Dublin, Belfield, Dublin 4, Ireland, and LAMA, UMR 5127 CNRS, Université de Savoie, Campus Scientifique, 73376 Le Bourget-du-Lac Cedex, France email: Denys.Dutykh@ucd.ie
DIDIER CLAMOND
Affiliation:
Laboratoire J.-A. Dieudonné, Université de Nice, Sophia Antipolis, Parc Valrose, 06108 Nice Cedex 2, France email: diderc@unice.fr
PAUL MILEWSKI
Affiliation:
Deptartment of Mathematical Sciences, University of Bath, Bath BA2 7JX, UK email: P.A.Milewski@bath.ac.uk
DIMITRIOS MITSOTAKIS
Affiliation:
University of California, Merced, 5200 North Lake Road, Merced, CA 94353, USA email: dmitsot@gmail.com
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Abstract

After we derive the Serre system of equations of water wave theory from a generalized variational principle, we present some of its structural properties. We also propose a robust and accurate finite volume scheme to solve these equations in one horizontal dimension. The numerical discretization is validated by comparisons with analytical and experimental data or other numerical solutions obtained by a highly accurate pseudo-spectral method.

Keywords

Serre equationsFinite volumesUNO schemeIMEX schemeSpectral methodsEuler equationsFree surface flows

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Type
Papers
Information
European Journal of Applied Mathematics , Volume 24 , Issue 5 , October 2013 , pp. 761 - 787
Copyright
Copyright © Cambridge University Press 2013 

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