A quasi-Hamiltonian discretization of the thermal shallow water equations

JOURNAL OF COMPUTATIONAL PHYSICS

卷:379

Article

Eldred, Christopher¹  Dubos, Thomas²  Kritsikis, Evaggelos³ 

[1] Univ Grenoble Alpes, Inria, CNRS, Grenoble INP,LJK, F-38000 Grenoble, France

[2] Paris Saclay Univ, Lab Meteorol Dynam, IPSL, Ecole Polytech, F-91120 Palaiseau, France

[3] Univ Paris 13, Lab Anal Geometrie & Applicat, F-93430 Villetaneuse, France

关键词: Thermal shallow water equations;    Dynamical core;    Mixed finite elements;    Finite element exterior calculus;    Mimetic Galerkin differences;    Hamiltonian mechanics;   

DOI  :  10.1016/j.jcp.2018.10.038

来源: Elsevier

【 摘 要 】

The rotating shallow water (RSW) equations are the usual testbed for the development of numerical methods for three-dimensional atmospheric and oceanic models. However, an arguably more useful set of equations are the thermal shallow water equations (TSW), which introduce an additional thermodynamic scalar but retain the single layer, two-dimensional structure of the RSW. As a stepping stone towards a three-dimensional atmospheric dynamical core, this work presents a quasi-Hamiltonian discretization of the thermal shallow water equations using compatible Galerkin methods, building on previous work done for the shallow water equations. Structure-preserving or quasi-Hamiltonian discretizations methods, that discretize the Hamiltonian structure of the equations of motion rather than the equations of motion themselves, have proven to be a powerful tool for the development of models with discrete conservation properties. By combining these ideas with an energy-conserving Poisson time integrator and a careful choice of Galerkin spaces, a large set of desirable properties can be achieved. In particular, for the first time total mass, buoyancy and energy are conserved to machine precision in the fully discrete model. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

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