Articles | Volume 9, issue 5
Development and technical paper
01 Jun 2016
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

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.

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.