Abstract
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.
Highlights
Introduction and MotivationLatitude-longitude grids over the sphere have been popular for use in the dynamical cores of numerical weather prediction models due to the orthogonality of the meridians and circles of latitude
These are finite element methods in which the variables lie in different function spaces, such that the discrete equations replicate the vector calculus identities of the continuous equations, such as ∇×∇f = 0 and ∇ · ∇ × f = 0. [2] showed for the linear rotating shallow-water equations that a compatible finite element discretisation, which facilitates the use of non-orthogonal meshes, still maintains many of the properties of [1]
The main result of this paper is the presentation of a model solving the three dimensional moist compressible Euler equations within this compatible finite element framework
Summary
Latitude-longitude grids over the sphere have been popular for use in the dynamical cores of numerical weather prediction models due to the orthogonality of the meridians and circles of latitude. This orthogonality can be exploited to gain a number of desirable numerical properties [1]. The model presented in this paper is written as part of Gusto, a library for dynamical cores using compatible finite element discretisations. Gusto itself is based on the Firedrake software of [7], the development of which is based at Imperial College London This software provides automated code generation for finite element methods. Firedrake has the functionality for tensor product element and extruded mesh functionality, as described in [8], [9] and [10], which we used substantially
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