10 papers
Entropy-Stable and Well-Balanced Discontinuous Galerkin Methods for the Compressible Euler Equations in Vector-Invariant Form
Marco Artiano, Kieran Ricardo, Oswald Knoth +2
We develop structure-preserving methods for the compressible Euler equations with gravity in vector-invariant form and potential temperature as a prognostic variable within the flu…
Data driven non-equilibrium moist phase exchanges for atmospheric convection within a discontinuous Galerkin model of the compressible Euler equations
David Lee, Kieran Ricardo, Junwei Lyu
A discrete formulation of the multiphase moist compressible Euler equations is presented for which the energy and tracer variance conserving dynamics is coupled to the non-equilibr…
High order tracer variance stable transport with low order energy conserving dynamics for the thermal shallow water equations
David Lee, Kieran Ricardo, Tamara Tambyah
A high order discontinuous Galerkin method for the material transport of thermodynamic tracers is coupled to a low order mixed finite element solver in the context of the thermal s…
Scalable ADER-DG Transport Method with Polynomial Order Independent CFL Limit
Kieran Ricardo, Kenneth Duru
Discontinuous Galerkin (DG) methods are known to suffer from increasingly restrictive explicit time-step constraints as the polynomial order increases, limiting their efficiency at…
Thermodynamic consistency and structure-preservation in summation by parts methods for the moist compressible Euler equations
Kieran Ricardo, David Lee, Kenneth Duru
Moist thermodynamics is a fundamental driver of atmospheric dynamics across all scales, making accurate modeling of these processes essential for reliable weather forecasts and cli…
Helmholtz preconditioning for the compressible Euler equations using mixed finite elements with Lorenz staggering
David Lee, Alberto F. Martín, Kieran Ricardo
Implicit solvers for atmospheric models are often accelerated via the solution of a preconditioned system. For block preconditioners this typically involves the factorisation of th…
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…