Simulation of shallow-water jets with a unified element-based continuous/discontinuous Galerkin model with grid flexibility on the sphere
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Authors
Marras, S.
Kopera, M.A.
Giraldo, F.X.
Subjects
reduced lat-lon grids
icosahedral grid
cubed-sphere
shallow-water equations
spectral element method
discontinuous Galerkin
grid generation on the sphere
transfinite interpolation
icosahedral grid
cubed-sphere
shallow-water equations
spectral element method
discontinuous Galerkin
grid generation on the sphere
transfinite interpolation
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Date of Issue
2014
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Abstract
We test the behaviour of a unified continuous/discontinuous Galerkin (CG/DG) shallowwater
model in spherical geometry with curved elements on three different grids
of ubiquitous use in atmospheric modelling: (i) the cubed-sphere, (ii) the reduced
latitude–longitude, and (iii) the icosahedral grid. Both conforming and non-conforming
grids are adopted including static and dynamically adaptive grids for a total of twelve mesh
configurations. The behaviour of CG and DG on the different grids are compared for a
nonlinear midlatitude perturbed jet and for a linear case that admits an analytic solution.
Because the inviscid solution on certain grids shows a high sensitivity to the resolution,
the viscous counterpart of the governing equations is also solved and the results compared.
The logically unstructured element-based CG/DG model described in this article is flexible
with respect to arbitrary grids. However, we were unable to define a best grid configuration
that could possiblyminimize the error regardless of the characteristic geometry of the flow.
This is especially true if the governing equations are not regularized by the addition of a
sufficiently large, fully artificial, diffusion mechanism, as will be shown. The main novelty
of this study lies in the unified implementation of two element-based Galerkin methods
that share the same numericalmachinery and do not rely on any specific grid configuration
to solve the shallow-water equation on the sphere.
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Article
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The article of record as published may be located at http://dx.doi.org/10.1002/qj.2474
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Applied Mathematics
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The authors gratefully acknowledge the support of the Office of Naval Research through program element PE-0602435N, the National Science Foundation (Division ofMathematical Sciences) through program element 121670, and the Air Force Office of Scientific Research through the Computational Mathematics program.
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Q. J. R. Meteorol. Soc. (2014) DOI:10.1002/qj.2474
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This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.