Finite volume and pseudo-spectral schemes for the fully nonlinear 1D Serre equations - Archive ouverte HAL Access content directly
Journal Articles European Journal of Applied Mathematics Year : 2013

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

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, experimental data or other numerical solutions obtained by a highly accurate pseudo-spectral method.
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Dates and versions

hal-00587994 , version 1 (22-04-2011)
hal-00587994 , version 2 (17-07-2011)
hal-00587994 , version 3 (23-07-2012)
hal-00587994 , version 4 (12-02-2013)

Licence

Attribution - NonCommercial - ShareAlike - CC BY 4.0

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Denys Dutykh, Didier Clamond, Paul Milewski, Dimitrios Mitsotakis. Finite volume and pseudo-spectral schemes for the fully nonlinear 1D Serre equations. European Journal of Applied Mathematics, 2013, 24 (5), pp.761-787. ⟨10.1017/S0956792513000168⟩. ⟨hal-00587994v4⟩
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