25 citations · 53 across the 8 of their papers we have counts for
8 papers
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…
A Comparison of Rosenbrock-Wanner and Crank-Nicolson Time Integrators for Atmospheric Modelling
David Lee
Non-hydrostatic atmospheric models often use semi-implicit temporal discretisations in order to negate the time step limitation of explicitly resolving the fast acoustic and gravit…
A comparison of variational upwinding schemes for geophysical fluids, and their application to potential enstrophy conserving discretisations
David Lee, Alberto F. Martín, Christopher Bladwell +1
Methods for upwinding the potential vorticity in a compatible finite element discretisation of the rotating shallow water equations are studied. These include the well-known antici…
Functional Calculus via the extension technique: a first hitting time approach
Daniel Hauer, David Lee
In this article, we present a solution to the problem: "Which type of linear operators can be realized by the Dirichlet-to-Neumann operator associated with the operator $-Δ-a(z)\fr…
Exact spatial and temporal balance of energy exchanges within a horizontally explicit/vertically implicit non-hydrostatic atmosphere
David Lee, Artur Palha
A new horizontally explicit/vertically implicit (HEVI) time splitting scheme for atmospheric modelling is introduced, for which the horizontal divergence terms are applied within t…
An energetically balanced, quasi-Newton integrator for non-hydrostatic vertical atmospheric dynamics
David Lee
An energetically balanced, implicit integrator for non-hydrostatic vertical atmospheric dynamics on the sphere is presented. The integrator allows for the exact balance of energy e…
Petrov-Galerkin flux upwinding for mixed mimetic spectral elements, and its application to geophysical flow problems
David Lee
Upwinded mass fluxes are described and analysed for advection operators discretised using mixed mimetic spectral elements. This involves a Petrov-Galerkin formulation by which the…
Discrete conservation properties for shallow water flows using mixed mimetic spectral elements
David Lee, Artur Palha, Marc Gerritsma
A mixed mimetic spectral element method is applied to solve the rotating shallow water equations. The mixed method uses the recently developed spectral element histopolation functi…