112 citations · 229 across the 11 of their papers we have counts for
12 papers
Exploring physics-dynamics coupling using moist shallow water equations
Nell Hartney, Thomas M. Bendall, Jemma Shipton
One of the key choices for numerical models of geophysical fluids is how parametrisations of physical processes interact with the numerical methods that handle the resolved flow, k…
Splitting horizontal and vertical polynomial order in a compatible finite element discretisation for numerical weather prediction
Daniel Witt, Thomas Bendall, Jemma Shipton
The accurate and efficient representation of atmospheric dynamics remains a central challenge in numerical weather prediction. A particular difficulty arises from the strong anisot…
Fast-wave slow-wave spectral deferred correction methods applied to the compressible Euler equations
Alex Brown, Joscha Fregin, Thomas Bendall +3
This paper investigates the application of a fast-wave slow-wave spectral deferred correction time-stepping method (FWSW-SDC) to the compressible Euler equations. The resulting mod…
Exploring forms of the moist shallow water equations using a new compatible finite element discretisation
Nell Hartney, Thomas M. Bendall, Jemma Shipton
The moist shallow water equations offer a promising route for advancing understanding of the coupling of physical parametrisations and dynamics in numerical atmospheric models, an…
The effect of linear dispersive errors on nonlinear timestepping accuracy in the f-plane rotating shallow water equations
Timothy C. Andrews, Jemma Shipton, Beth A. Wingate
For simulations of time evolution problems, such as weather and climate models, taking the largest stable timestep is advantageous for reducing wall-clock time. A drawback of doing…
A compatible finite element discretisation for the nonhydrostatic vertical slice equations
C. J. Cotter, J. Shipton
We present a compatible finite element discretisation for the vertical slice compressible Euler equations, at next-to-lowest order (i.e., the pressure space is bilinear discontinuo…
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…
The Recovered Space Advection Scheme for Lowest-Order Compatible Finite Element Methods
Thomas M. Bendall, Colin J. Cotter, Jemma Shipton
We present a new compatible finite element advection scheme for the compressible Euler equations. Unlike the discretisations described in Cotter and Kuzmin (2016) and Shipton et al…
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…
Vertical slice modelling of nonlinear Eady waves using a compatible finite element method
Hiroe Yamazaki, Jemma Shipton, Michael J. P. Cullen +2
A vertical slice model is developed for the Euler-Boussinesq equations with a constant temperature gradient in the direction normal to the slice (the Eady-Boussinesq model). The mo…
High level implementation of geometric multigrid solvers for finite element problems: applications in atmospheric modelling
Lawrence Mitchell, Eike Hermann Müller
The implementation of efficient multigrid preconditioners for elliptic partial differential equations (PDEs) is a challenge due to the complexity of the resulting algorithms and co…
Mixed finite elements for numerical weather prediction
C. J. Cotter, J. Shipton
We show how two-dimensional mixed finite element methods that satisfy the conditions of finite element exterior calculus can be used for the horizontal discretisation of dynamical…