A SOLUTION OF THE CONSERVATION LAW FORM OF THE SERRE EQUATIONS

DOI10.1017/S144618111600002XzbMath1426.76081OpenAlexW2315502791MaRDI QIDQ5369450

Stephen G. Roberts, C. Zoppou, Jordan P. A. Pitt

Publication date: 17 October 2017

Published in: The ANZIAM Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s144618111600002x

zbMATH Keywords

conservation lawsdispersive wavesSerre equationsfinite-volume method

Mathematics Subject Classification ID

Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) Finite difference methods applied to problems in fluid mechanics (76M20) Finite volume methods applied to problems in fluid mechanics (76M12)

Related Items (3)

Behaviour of the Serre equations in the presence of steep gradients revisited ⋮ Numerical scheme for the generalised Serre-Green-Naghdi model ⋮ Numerical solution of the fully non-linear weakly dispersive Serre equations for steep gradient flows

Cites Work

• High order well-balanced CDG-FE methods for shallow water waves by a Green-Naghdi model
• Numerical simulation of strongly nonlinear and dispersive waves using a Green-Naghdi model
• A numerical study of diagonally split Runge-Kutta methods for PDEs with discontinuities
• Discontinuous Galerkin methods for solving Boussinesq-Green-Naghdi equations in resolving non-linear and dispersive surface water waves
• Asymptotic description of solitary wave trains in fully nonlinear shallow-water theory
• High resolution schemes for hyperbolic conservation laws
• Efficient implementation of essentially nonoscillatory shock-capturing schemes
• The kinematics and stability of solitary and cnoidal wave solutions of the Serre equations
• Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov's method
• Semidiscrete Central-Upwind Schemes for Hyperbolic Conservation Laws and Hamilton--Jacobi Equations
• A derivation of equations for wave propagation in water of variable depth
• Korteweg-de Vries Equation and Generalizations. III. Derivation of the Korteweg-de Vries Equation and Burgers Equation

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