74 citations · 105 across the 29 of their papers we have counts for
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An entropy stable discontinuous Galerkin method for the spherical thermal shallow water equations
Kieran Ricardo, Kenneth Duru, David Lee
We present a novel discontinuous Galerkin finite element method for numerical simulations of the rotating thermal shallow water equations in complex geometries using curvilinear me…
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…
A provably stable numerical method for the anisotropic diffusion equation in confined magnetic fields
Dean Muir, Kenneth Duru, Matthew Hole +1
We present a novel numerical method for solving the anisotropic diffusion equation in magnetic fields confined to a periodic box which is accurate and provably stable. We derive en…
Entropy and energy conservation for thermal atmospheric dynamics using mixed compatible finite elements
Kieran Ricardo, David Lee, Kenneth Duru
Atmospheric systems incorporating thermal dynamics must be stable with respect to both energy and entropy. While energy conservation can be enforced via the preservation of the ske…
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…
Conservation and stability in a discontinuous Galerkin method for the vector invariant spherical shallow water equations
Kieran Ricardo, David Lee, Kenneth Duru
We develop a novel and efficient discontinuous Galerkin spectral element method (DG-SEM) for the spherical rotating shallow water equations in vector invariant form. We prove that…
An efficient method for the anisotropic diffusion equation in magnetic fields
Dean Muir, Kenneth Duru, Matthew Hole +1
We solve the anisotropic diffusion equation in 2D, where the dominant direction of diffusion is defined by a vector field which does not conform to a Cartesian grid. Our method use…