15 January 2018

The Staggered Nodal Finite Element Method (SNFEM) Discretization for Non-Hydrostatic Atmospheric Modeling

Science

We present a new discrete representation of non-hydrostatic vertical motions in the atmosphere based on a generalization of grid staggering to finite elements. The result is a model that is efficiently implemented in parallel, is arbitrarily accurate in space, and shows superior wave dispersion properties as a consequence of staggering variables in the column. Several test case results show accurate performance through a range of scales from planetary to convective eddies on the order of 10 meters.

Impact

The atmospheric model given here aims to balance efficiency, accuracy, and ease of implementation. We have accomplished this by combining new and tested mathematical and numerical methods with an emphasis on computational speed with minimal tradeoffs in accuracy.  The model also provides a testbed for improved methods and different formulations of the governing equations.

Summary

The Staggered Nodal Finite Element Method is a generalization of grid staggering to finite element methods. We present a column-wise vertical discretization in the SNFEM combined with quadrilateral spectral elements in the horizontal directions. The result is a model with a straight forward parallel implementation and a framework for testing purely vertical discretizations (with and without staggering) with the goal of capturing high-resolution non-hydrostatic phenomena in the atmosphere. Furthermore, the model incorporates an Implicit/Explicit (IMEX) construction allowing for extensive testing of time integration schemes. As a relatively compact and monolithic software, our model allows for rapid testing and development of candidate methods that may be used to advance a non-hydrostatic version of ACME.The Staggered Nodal Finite Element Method is a generalization of grid staggering to finite element methods. We present a column-wise vertical discretization in the SNFEM combined with quadrilateral spectral elements in the horizontal directions. The result is a model with a straight forward parallel implementation and a framework for testing purely vertical discretizations (with and without staggering) with the goal of capturing high resolution non-hydrostatic phenomena in the atmosphere. Furthermore, the model incorporates an Implicit/Explicit (IMEX) construction allowing for extensive testing of time integration schemes. As a relatively compact and monolithic software, our model allows for rapid testing and development of candidate methods that may be used to advance a non-hydrostatic version of ACME.

Contact
Jorge E. Guerra
University of California Davis
Funding
Programs
Publications
Ullrich, PA.  2016.  "A High-Order Staggered Finite-Element Vertical Discretization for Non-Hydrostatic Atmospheric Models."  Geoscientific Model Development 9(5): 2007-2029, doi:10.5194/gmd-9-2007-2016.