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Title: A high-order staggered finite-element vertical discretization for non-hydrostatic atmospheric models

Abstract

Atmospheric modeling systems require economical methods to solve the non-hydrostatic Euler equations. Two major differences between hydrostatic models and a full non-hydrostatic description lies in the vertical velocity tendency and numerical stiffness associated with sound waves. In this work we introduce a new arbitrary-order vertical discretization entitled the staggered nodal finite-element method (SNFEM). Our method uses a generalized discrete derivative that consistently combines the discontinuous Galerkin and spectral element methods on a staggered grid. Our combined method leverages the accurate wave propagation and conservation properties of spectral elements with staggered methods that eliminate stationary (2Δx) modes. Furthermore, high-order accuracy also eliminates the need for a reference state to maintain hydrostatic balance. In this work we demonstrate the use of high vertical order as a means of improving simulation quality at relatively coarse resolution. We choose a test case suite that spans the range of atmospheric flows from predominantly hydrostatic to nonlinear in the large-eddy regime. Lastly, our results show that there is a distinct benefit in using the high-order vertical coordinate at low resolutions with the same robust properties as the low-order alternative.

Authors:
;
Publication Date:
Research Org.:
Univ. of California, Davis, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1255170
Alternate Identifier(s):
OSTI ID: 1268264
Grant/Contract Number:  
SC0014669
Resource Type:
Published Article
Journal Name:
Geoscientific Model Development (Online)
Additional Journal Information:
Journal Name: Geoscientific Model Development (Online) Journal Volume: 9 Journal Issue: 5; Journal ID: ISSN 1991-9603
Publisher:
Copernicus Publications, EGU
Country of Publication:
Germany
Language:
English
Subject:
54 ENVIRONMENTAL SCIENCES; step integration methods; navier-stokes equations; shallow-water equations; optimal representation; spectral element; prediction

Citation Formats

Guerra, Jorge E., and Ullrich, Paul A. A high-order staggered finite-element vertical discretization for non-hydrostatic atmospheric models. Germany: N. p., 2016. Web. https://doi.org/10.5194/gmd-9-2007-2016.
Guerra, Jorge E., & Ullrich, Paul A. A high-order staggered finite-element vertical discretization for non-hydrostatic atmospheric models. Germany. https://doi.org/10.5194/gmd-9-2007-2016
Guerra, Jorge E., and Ullrich, Paul A. Wed . "A high-order staggered finite-element vertical discretization for non-hydrostatic atmospheric models". Germany. https://doi.org/10.5194/gmd-9-2007-2016.
@article{osti_1255170,
title = {A high-order staggered finite-element vertical discretization for non-hydrostatic atmospheric models},
author = {Guerra, Jorge E. and Ullrich, Paul A.},
abstractNote = {Atmospheric modeling systems require economical methods to solve the non-hydrostatic Euler equations. Two major differences between hydrostatic models and a full non-hydrostatic description lies in the vertical velocity tendency and numerical stiffness associated with sound waves. In this work we introduce a new arbitrary-order vertical discretization entitled the staggered nodal finite-element method (SNFEM). Our method uses a generalized discrete derivative that consistently combines the discontinuous Galerkin and spectral element methods on a staggered grid. Our combined method leverages the accurate wave propagation and conservation properties of spectral elements with staggered methods that eliminate stationary (2Δx) modes. Furthermore, high-order accuracy also eliminates the need for a reference state to maintain hydrostatic balance. In this work we demonstrate the use of high vertical order as a means of improving simulation quality at relatively coarse resolution. We choose a test case suite that spans the range of atmospheric flows from predominantly hydrostatic to nonlinear in the large-eddy regime. Lastly, our results show that there is a distinct benefit in using the high-order vertical coordinate at low resolutions with the same robust properties as the low-order alternative.},
doi = {10.5194/gmd-9-2007-2016},
journal = {Geoscientific Model Development (Online)},
number = 5,
volume = 9,
place = {Germany},
year = {2016},
month = {6}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
https://doi.org/10.5194/gmd-9-2007-2016

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Cited by: 1 work
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