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

D. Dutykh, D. Clamond, P. Milewski, D. Mitsotakis

Research output: Contribution to journalArticle

32 Citations (Scopus)

### 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.
Original language English 761-787 27 European Journal of Applied Mathematics 24 5 24 May 2013 https://doi.org/10.1017/S0956792513000168 Published - Oct 2013

### Fingerprint

Generalized Variational Principle
Pseudospectral Method
Finite Volume Scheme
Fully Nonlinear
Water waves
Water Waves
Finite Volume
Structural Properties
System of equations
Structural properties
Horizontal
Discretization
Numerical Solution
Experimental Data

### Cite this

Finite volume and pseudo-spectral schemes for the fully nonlinear 1D Serre equations. / Dutykh, D.; Clamond, D.; Milewski, P.; Mitsotakis, D.

In: European Journal of Applied Mathematics, Vol. 24, No. 5, 10.2013, p. 761-787.

Research output: Contribution to journalArticle

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