4 papers · 1 filter
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…
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…
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…