Efficient Construction of Unified Continuous and Discontinuous Galerkin Formulations for the 3D Euler Equations
Abstract
A unified approach for the numerical solution of the 3D hyperbolic Euler equations using high order methods,
namely continuous Galerkin (CG) and discontinuous Galerkin (DG) methods, is presented. First, we examine
how classical CG that uses a global storage scheme can be constructed within the DG framework using
constraint imposition techniques commonly used in the finite element literature. Then, we implement and
test a simplified version in the Non-hydrostatic Unified Model of the Atmosphere (NUMA) for the case of
explicit time integration and a diagonal mass matrix. Constructing CG within the DG framework allows CG
to benefit from the desirable properties of DG such as, easier hp-refinement, better stability etc. Moreover,
this representation allows for regional mixing of CG and DG depending on the
flow regime in an area. The
different
flavors of CG and DG in the unified implementation are then tested for accuracy and performance
using a suite of benchmark problems representative of cloud-resolving scale, meso-scale and global-scale
atmospheric dynamics. The value of our unified approach is that we are able to show how to carry both CG
and DG methods within the same code and also offer a simple recipe for modifying an existing CG code to
DG and vice versa.
Description
Preprint submitted to TBD
Rights
This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.Collections
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