Hybridised finite element methods for environmental flows over topography

This project is researching a hybridisable finite element discretisation for environmental flows (such as the compressible rotating Euler equations) over topography. In the last 8 years we have developed compatible finite element methods for environmental flows which have been adopted by the Met Office in their atmosphere model. One of the drawbacks of these methods is that they do not cleanly separate into vertical and horizontal velocities on terrain-following meshes, leading to artefacts around sharp topography. In this project we are designing a new discretisation based upon hybridisable discontinuous Galerkin methods that makes this separation clear. The discretisation uses pressure-robust reconstruction in the Coriolis term to preserve the geostrophic balance properties of the compatible finite element method. In the project we will design, analyse and implement these new methods. This project aligns with the strategic theme of mathematical science within the numerical analysis research area.