Development and Evaluation of a Hydrostatic Dynamical Core Using the Spectral Element/Discontinuous Galerkin Methods

Abstract

In this paper, we present a dynamical core for the atmospheric primitive hydrostatic equations using a unified formulation of spectral element (SE) and discontinuous Galerkin (DG) methods in the horizontal direction with a finite difference \(FD) method in the radial direction. The CG and DG horizontal discretization employs high-order nodal basis functions associated with Lagrange polynomials based on Gauss-Lobatto-Legendre (GLL) quadrature points, which define the common machinery. The atmospheric primitive hydrostatic equations are solved on the cubed-sphere grid using the flux form governing equations three-dimensional (3D) Cartesian space. By using Cartesian space, we can avoid the pole singularity problem due to spherical coordinates and this also allows us to use any quadrilateral-based grid naturally. In order to consider an easy way for coupling the dynamics with existing physics packages, we use a FD in the radial direction. The models are verified by conducting conventional benchmark test cases: the Rossby-Haurwitz wavenumber 4 Jablonowski-Williamson tests for balanced initial state and baroclinic instability, and Held- Suarez tests. The results from those tests demonstrate that the present dynamical core can produce numerical solutions of good quality comparable to other models.

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Document Details

Document Type
Technical Report
Publication Date
Apr 01, 2014
Accession Number
ADA604581

Entities

People

  • Francis Giraldo
  • Suk-jin Choi

Organizations

  • Naval Postgraduate School

Tags

Communities of Interest

  • Cyber

DTIC Thesaurus Topics

  • Applied Mathematics
  • Couplings
  • Differential Equations
  • Dynamics
  • Equations
  • Fluids
  • Galerkin Method
  • Geometry
  • Grids
  • Instability
  • Mathematics
  • Physics
  • Polynomials
  • Shallow Water
  • Simulations
  • Stratified Fluids
  • Three Dimensional

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)

Technology Areas

  • Space