11 papers
An intrinsic finite element framework for scalar- and vector-valued partial differential equations on general manifolds
Tamara A. Tambyah, Alberto F. Martín, David Lee +1
We present an intrinsic finite element framework for the numerical approximation of scalar- and vector-valued partial differential equations on general manifolds described by atlas…
GridapGeosciences.jl: A Julia finite element package for partial differential equations on general manifolds
Tamara A. Tambyah, Alberto F. Martín, David Lee +1
We present GridapGeosciencesjl, a new parallel distributed-memory Julia package for the numerical approximation of partial differential equations on general manifolds. Our abstr…
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…
A perfectly matched layer for damping vertically propagating waves in the compressible Boussinesq equations
Timothy C. Andrews, Kenneth Duru, David Lee
This paper introduces a new application of the perfectly matched layer (PML) for mitigating model top wave reflections in geophysical fluid models. Typically, a strong Laplacian or…
Consistency analysis for combined homogenization and shallow water limit of water waves
Antoine Gloria, David Lee
We consider a shallow water model in a homogenization framework. For periodic topographies, Craig, Lannes and Sulem have established a consistency result under some non-resonance c…
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…
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…
Energy and entropy conserving compatible finite elements with upwinding for the thermal shallow water equations
Tamara A. Tambyah, David Lee, Santiago Badia
In this work, we develop a new compatible finite element formulation of the thermal shallow water equations that conserves energy and mathematical entropies given by buoyancy-relat…
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…
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…