Continuous and Discontinuous Galerkin Methods for a Scalable 3D Nonhydrostatic Atmospheric Model: limited-area mode

Abstract

This paper describes a unified, element based Galerkin (EBG) framework for a three-dimen- sional, nonhydrostatic model for the atmosphere. In general, EBG methods possess high- order accuracy, geometric flexibility, excellent dispersion properties and good scalability. Our nonhydrostatic model, based on the compressible Euler equations, is appropriate for both limited-area and global atmospheric simulations. Both a continuous Galerkin (CG), or spectral element, and discontinuous Galerkin (DG) model are considered using hexahe- dral elements. The formulation is suitable for both global and limited-area atmospheric modeling, although we restrict our attention to 3D limited-area phenomena in this study; global atmospheric simulations will be presented in a follow-up paper. Domain decompo- sition and communication algorithms used by both our CG and DG models are presented. The communication volume and exchange algorithms for CG and DG are compared and contrasted. Numerical verification of the model was performed using two test cases: flow past a 3D mountain and buoyant convection of a bubble in a neutral atmosphere; these tests indicate that both CG and DG can simulate the necessary physics of dry atmospheric dynamics. Scalability of both methods is shown up to 8192 CPU cores, with near ideal scal- ing for DG up to 32,768 cores.