A High-Order Staggered Finite-Element Vertical Discretization for Non-Hydrostatic Atmospheric Models

TitleA High-Order Staggered Finite-Element Vertical Discretization for Non-Hydrostatic Atmospheric Models
Publication TypeJournal Article
Year of Publication2016
JournalGeoscientific Model Development
Volume9
Number5
Pages2007-2029
Date Published06/2016
Abstract / Summary

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 lie 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 (2dx) 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. 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.

URLhttp://dx.doi.org/10.5194/gmd-9-2007-2016
DOI10.5194/gmd-9-2007-2016
Journal: Geoscientific Model Development
Year of Publication: 2016
Volume: 9
Number: 5
Pages: 2007-2029
Date Published: 06/2016

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 lie 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 (2dx) 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. 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
Citation:
Ullrich, PA.  2016.  "A High-Order Staggered Finite-Element Vertical Discretization for Non-Hydrostatic Atmospheric Models."  Geoscientific Model Development 9(5): 2007-2029.  https://doi.org/10.5194/gmd-9-2007-2016.