A compatible finite‐element discretisation for the moist compressible Euler equations

A promising development of the last decade in the numerical modelling of geophysical fluids has been the compatible finite‐element framework. Indeed, this will form the basis for the next‐generation dynamical core of the Met Office. For this framework to be useful for numerical weather prediction models, it must be able to handle descriptions of unresolved and diabatic processes. These processes offer a challenging test for any numerical discretisation, and have not yet been described within the compatible finite‐element framework. The main contribution of this article is to extend a discretisation using this new framework to include moist thermodynamics. Our results demonstrate that discretisations within the compatible finite‐element framework can be robust enough also to describe moist atmospheric processes. We describe our discretisation strategy, including treatment of moist processes, and present two configurations of the model using different sets of function spaces with different degrees of finite element. The performance of the model is demonstrated through several test cases. Two of these test cases are new cloudy‐atmosphere variants of existing test cases: inertia–gravity waves in a two‐dimensional vertical slice and a three‐dimensional rising thermal. We present a new discretisation of the moist compressible Euler equations, using a compatible finite‐element framework. As well as detailing the discretisation using configurations with two different sets of function spaces, we demonstrate it through some test cases. A comparison of the two configurations is shown in the figure, which presents the θe field from a rising thermal with (top) the lower order function spaces and (bottom) the higher order function spaces.