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. doi: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 = {Wed Jun 01 00:00:00 EDT 2016},
month = {Wed Jun 01 00:00:00 EDT 2016}
}
https://doi.org/10.5194/gmd-9-2007-2016
Web of Science
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