45 citations · 132 across the 7 of their papers we have counts for
7 papers
Hybridised multigrid preconditioners for a compatible finite element dynamical core
Jack D. Betteridge, Colin J. Cotter, Thomas H. Gibson +3
Compatible finite element discretisations for the atmospheric equations of motion have recently attracted considerable interest. Semi-implicit timestepping methods require the repe…
Large-eddy simulations with ClimateMachine: a new open-source code for atmospheric simulations on GPUs and CPUs
Akshay Sridhar, Yassine Tissaoui, Simone Marras +11
We introduce ClimateMachine, a new open-source atmosphere modeling framework using the Julia language to be performance portable on central processing units (CPUs) and graphics pro…
Entropy Stable Discontinuous Galerkin Methods for Balance Laws in Non-Conservative Form: Applications to the Euler Equations with Gravity
Maciej Waruszewski, Jeremy E. Kozdon, Lucas C. Wilcox +2
In this work a non-conservative balance law formulation is considered that encompasses the rotating, compressible Euler equations for dry atmospheric flows. We develop a semi-discr…
Multigrid preconditioners for the hybridized Discontinuous Galerkin discretisation of the shallow water equations
Jack D. Betteridge, Thomas H. Gibson, Ivan G. Graham +1
Numerical climate- and weather-prediction requires the fast solution of the equations of fluid dynamics. Discontinuous Galerkin (DG) discretisations have several advantageous prope…
A Compatible Finite Element Discretisation for the Moist Compressible Euler Equations
Thomas M. Bendall, Thomas H. Gibson, Jemma Shipton +2
We present new discretisation of the moist compressible Euler equations, using the compatible finite element framework identified in Cotter and Shipton (2012). The discretisation s…
Slate: extending Firedrake's domain-specific abstraction to hybridized solvers for geoscience and beyond
Thomas H. Gibson, Lawrence Mitchell, David A. Ham +1
Within the finite element community, discontinuous Galerkin (DG) and mixed finite element methods have become increasingly popular in simulating geophysical flows. However, robust…
Higher-order compatible finite element schemes for the nonlinear rotating shallow water equations on the sphere
J. Shipton, T. H. Gibson, C. J. Cotter
We describe a compatible finite element discretisation for the shallow water equations on the rotating sphere, concentrating on integrating consistent upwind stabilisation into the…