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

TL;DR

This paper derives the Serre equations from a variational principle, analyzes their properties, and introduces a robust finite volume scheme validated against analytical and experimental data, enhancing numerical solutions for water wave modeling.

Contribution

It presents a new finite volume scheme for the Serre equations, derived from fundamental principles, with validation against high-accuracy spectral methods and experimental data.

Findings

The scheme accurately captures water wave dynamics.

Validation shows strong agreement with analytical and experimental results.

Structural properties of the Serre system are analyzed.

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.