A mixed mimetic spectral element model of the 3D compressible Euler equations on the cubed sphere

Journal article (2020)

Authors

D Lee Monash University
A. Palha Aerodynamics - Aerospace Engineering
Research Group
Aerodynamics (Aerospace Engineering) (TU Delft)
Euler equations Mimetic Horizontally explicit/vertically implicit Cubed sphere Spectral element
More Info
expand_more

Published Date

15-01-2020

Language

English

Reuse Rights

Other than for strictly personal use, it is not permitted to download, forward or distribute the text or part of it, without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license such as Creative Commons.

Faculty

Aerospace Engineering

Department

Flow Physics and Technology

Research Group

Aerodynamics

Abstract

A model of the three-dimensional rotating compressible Euler equations on the cubed sphere is presented. The model uses a mixed mimetic spectral element discretization which allows for the exact exchanges of kinetic, internal and potential energy via the compatibility properties of the chosen function spaces. A Strang carryover dimensional splitting procedure is used, with the horizontal dynamics solved explicitly and the vertical dynamics solved implicitly so as to avoid the CFL restriction of the vertical sound waves. The function spaces used to represent the horizontal dynamics are discontinuous across vertical element boundaries, such that each horizontal layer is solved independently so as to avoid the need to invert a global 3D mass matrix, while the function spaces used to represent the vertical dynamics are similarly discontinuous across horizontal element boundaries, allowing for the serial solution of the vertical dynamics independently for each horizontal element. The model is validated against standard test cases for baroclinic instability within an otherwise hydrostatically and geostrophically balanced atmosphere, and a non-hydrostatic gravity wave as driven by a temperature perturbation.