Mixed finite elements for numerical weather prediction

JOURNAL OF COMPUTATIONAL PHYSICS

卷:231

Article

Cotter, C. J.¹  Shipton, J.¹ 

[1] Univ London Imperial Coll Sci Technol & Med, Dept Aeronaut, London SW7 2AZ, England

关键词: Mixed finite elements;    Stability;    Steady geostrophic states;    Geophysical fluid dynamics;    Numerical weather prediction;   

DOI  :  10.1016/j.jcp.2012.05.020

来源: Elsevier

【 摘 要 】

We show how mixed finite element methods that satisfy the conditions of finite element exterior calculus can be used for the horizontal discretisation of dynamical cores for numerical weather prediction on pseudo-uniform grids. This family of mixed finite element methods can be thought of in the numerical weather prediction context as a generalisation of the popular polygonal C-grid finite difference methods. There are a few major advantages: the mixed finite element methods do not require an orthogonal grid, and they allow a degree of flexibility that can be exploited to ensure an appropriate ratio between the velocity and pressure degrees of freedom so as to avoid spurious mode branches in the numerical dispersion relation. These methods preserve several properties of the C-grid method when applied to linear barotropic wave propagation, namely: (a) energy conservation, (b) mass conservation, (c) no spurious pressure modes, and (d) steady geostrophic modes on the f-plane. We explain how these properties are preserved, and describe two examples that can be used on pseudo-uniform grids: the recently-developed modified RTk-Q(k-1) element pairs on quadrilaterals and the BDFM1-P1(DG) element pair on triangles. All of these mixed finite element methods have an exact 2: 1 ratio of velocity degrees of freedom to pressure degrees of freedom. Finally we illustrate the properties with some numerical examples. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

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