Application of a Galerkin finite element scheme to atmospheric buoyant and gravity driven flows

Abstract

The application of a new finite element (FE) technique for the solution of stratified, non-hydrostatic, low-Mach number flows is introduced in the context of mesoscale atmospheric modeling. In this framework, a Compressible Variational Multiscale (VMS-C) finite element algorithm to solve the conservative form of the Euler equations coupled to the conservation of potential temperature was developed. This methodology is new in the fields of Computational Fluid Dynamics for compressible flows and in Numerical Weather Prediction (NWP), and we mean to show its ability to maintain stability in the solution of thermal, gravity-driven flows in a stratified environment. This effort is justified by the advantages offered by a Galerkin finite element algorithm when massive parallel efficiency is a constraint, which is indeed becoming the paradigm for both CFD and NWP practitioners. The algorithm is validated against the standard test cases specifically designed to test the dynamical core of new atmospheric models. In the context of buoyant and gravity flows three tests are selected among those presented in the literature: the warm rising smooth anomaly, and two versions of the density current evolution from a cold disturbance defined by different initial conditions. The reference quantitative and qualitative values are taken from the literature and from the output obtained with the Weather Research and Forecasting model (WRF-ARW), a state-of-the-art research NWP model.