Journal cover Journal topic
Geoscientific Model Development An interactive open-access journal of the European Geosciences Union
Geosci. Model Dev., 9, 2007-2029, 2016
https://doi.org/10.5194/gmd-9-2007-2016
© Author(s) 2016. This work is distributed under
the Creative Commons Attribution 3.0 License.
Development and technical paper
01 Jun 2016
A high-order staggered finite-element vertical discretization for non-hydrostatic atmospheric models
Jorge E. Guerra and Paul A. Ullrich Department of Land, Air and Water Resources, University of California, Davis, One Shields Ave., Davis, CA 95616, USA
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. 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.

Citation: Guerra, J. E. and Ullrich, P. A.: A high-order staggered finite-element vertical discretization for non-hydrostatic atmospheric models, Geosci. Model Dev., 9, 2007-2029, https://doi.org/10.5194/gmd-9-2007-2016, 2016.
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Short summary
This work introduces a collection of advances in the field of numerical simulation of the atmosphere using mixed finite element methods. We emphasize vertical motions in the atmosphere and apply state-of-the-art mathematics and programming paradigms to solve the differential equations that govern air flow cast in a coordinate-free formulation. The simulations show accurate flow features over a wide range of spatial scales including several important phenomena.
This work introduces a collection of advances in the field of numerical simulation of the...
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