5 papers
Strongly stable dual-pairing summation by parts finite difference schemes for the vector invariant nonlinear shallow water equations -- I: Numerical scheme and validation on the plane
Justin Kin Jun Hew, Kenneth Duru, Stephen Roberts +2
We present an energy/entropy stable and high order accurate finite difference (FD) method for solving the nonlinear (rotating) shallow water equations (SWEs) in vector invariant fo…
On well-posed boundary conditions and energy stable finite volume method for the linear shallow water wave equation
Rudi Prihandoko, Kenneth Duru, Stephen Roberts +1
We derive and analyse well-posed boundary conditions for the linear shallow water wave equation. The analysis is based on the energy method and it identifies the number, location a…
Well-posed boundary conditions and energy stable discontinuous Galerkin spectral element method for the linearized Serre equations
Kenny Wiratama, Kenneth Duru, Stephen Roberts +1
We derive well-posed boundary conditions for the linearized Serre equations in one spatial dimension by utilizing the energy method. An energy stable and conservative discontinuous…
Behaviour of the Serre Equations in the Presence of Steep Gradients Revisited
Jordan Pitt, Christopher Zoppou, Stephen Roberts
We use numerical methods to study the behaviour of the Serre equations in the presence of steep gradients because there are no known analytical solutions for these problems. In kee…
Third-order Finite Volume/Finite Element Solution of the Fully Nonlinear Weakly Dispersive Serre Equations
Christopher Zoppou, Jordan Pitt, Stephen G. Roberts
The nonlinear weakly dispersive Serre equations contain higher-order dispersive terms. This includes a mixed derivative flux term which is difficult to handle numerically. The mix…