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.

28 pages, 16 figures, 75 references. Other author's papers can be downloaded at http://www.denys-dutykh.com/

References in corpus (4)

• Finite volume schemes for dispersive wave propagation and runup
• Practical use of variational principles for modeling water waves
• Finite volume methods for unidirectional dispersive wave models
• Shallow water equations for large bathymetry variations

Cited by in corpus (19)

• Fully nonlinear long-waves models in presence of vorticity
• On the Galerkin / finite-element method for the Serre equations
• A modified Galerkin/finite element method for the numerical solution of the Serre-Green-Naghdi system
• Modified Shallow Water Equations for significantly varying seabeds
• On the Galilean invariance of some dispersive wave equations
• On the nonlinear dynamics of the traveling-wave solutions of the Serre system
• Non-dispersive conservative regularisation of nonlinear shallow water (and isothermal Euler) equations
• Mechanical balance laws for fully nonlinear and weakly dispersive water waves
• Numerical simulation of conservation laws with moving grid nodes: Application to tsunami wave modelling
• A new run-up algorithm based on local high-order analytic expansions
• Peregrine's system revisited
• On the multi-symplectic structure of the Serre-Green-Naghdi equations
• Asymptotic nonlinear and dispersive pulsatile flow in elastic vessels with cylindrical symmetry
• Coupling Conditions for Water Waves at Forks
• Numerical study of the Serre-Green-Naghdi equations and a fully dispersive counterpart
• Serre-type equations in deep water
• Nonlinear shallow-water waves with vertical odd viscosity
• Modeling water waves beyond perturbations
• On time relaxed schemes and formulations for dispersive wave equations