Showing math.NAShow all
3 papers · 1 filter
math.NA2023
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…
math.NA2023
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…
math.NA2023
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…