o3o3: A variant of spectral elements with a regular collocation grid

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Title: o3o3: A variant of spectral elements with a regular collocation grid
Authors: Steppeler, J
Li, J
Fang, F
Zhu, J
Ullrich, PA
Item Type: Journal Article
Abstract: In this study, an alternative local Galerkin method (LGM), the o3o3 scheme, is proposed. o3o3 is a variant or generalization of the third-order spectral element method (SEM3). It uses third-order piecewise polynomials for the representation of a field and piecewise third-degree polynomials for fluxes. For the discretization, SEM3 uses the irregular Legendre–Gauss–Lobatto grid while o3o3 uses a regular collocation grid. o3o3 can be regarded as an inhomogeneous finite-difference scheme on a uniform grid, which means that the finite-difference equations are different for each group with three points. A particular version of o3o3 is set as an example of many possibilities to construct LGM schemes on piecewise polynomial spaces in which the basis functions used are continuous at corner points and function spaces having continuous derivatives are shortly discussed. We propose a standard o3o3 scheme and a spectral o3o3 scheme as alternatives to the standard method of using the quadrature approximation. These two particular schemes selected were chosen for ease of implementation rather than optimal performance. In one dimension, compared to standard SEM3, o3o3 has a larger CFL condition benefiting from the use of a regular collocation grid. While SEM3 uses the irregular Legendre–Gauss–Lobatto collocation grid, o3o3 uses a regular grid. This is considered an advantage for physical parameterizations. The shortest resolved wave is marginally smaller than that with SEM3. In two dimensions, o3o3 is implemented on a sparse grid where only a part of the points on the underlying regular grid are used for forecasting.
Issue Date: 1-Jun-2019
Date of Acceptance: 9-Mar-2019
URI: http://hdl.handle.net/10044/1/70433
DOI: https://doi.org/10.1175/MWR-D-18-0288.1
ISSN: 0027-0644
Publisher: American Meteorological Society
Start Page: 2067
End Page: 2082
Journal / Book Title: Monthly Weather Review
Volume: 147
Issue: 6
Copyright Statement: 2019 American Meteorological Society. This article is licensed under a Creative Commons Attribution 4.0 license (http://creativecommons.org/ licenses/by/4.0/).
Sponsor/Funder: Engineering & Physical Science Research Council (E
Funder's Grant Number: RG80519
Keywords: Science & Technology
Physical Sciences
Meteorology & Atmospheric Sciences
Algorithms
Grid systems
Tracers
SHALLOW-WATER MODEL
Science & Technology
Physical Sciences
Meteorology & Atmospheric Sciences
Algorithms
Grid systems
Tracers
SHALLOW-WATER MODEL
Meteorology & Atmospheric Sciences
0401 Atmospheric Sciences
Publication Status: Published
Open Access location: https://journals.ametsoc.org/doi/full/10.1175/MWR-D-18-0288.1
Online Publication Date: 2019-05-15
Appears in Collections:Earth Science and Engineering



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