Efficient Construction of Unified Continuous and Discontinuous Galerkin Formulations for the 3D Euler Equations

Thumbnail Image
Files
Abdi_Giraldo_Efficient_Construction_2016.pdf (1.44 MB)
Authors
Abdi, Daniel S.
Giraldo, Francis X.
Subjects
NUMA
continuous Galerkin
discontinuous Galerkin
Advisors
Date of Issue
2016-05-28
Date
May 28, 2016
Publisher
Language
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.
Type
Article
Description
Preprint submitted to TBD
URI
https://hdl.handle.net/10945/49922
Series/Report No
Department
Applied Mathematics
Organization
Naval Postgraduate School (U.S.)
Identifiers
NPS Report Number
Sponsors
Office of Naval Research, PE-0602435N
Funder
Office of Naval Research, PE-0602435N
Format
29 p.
Citation
Distribution Statement
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
Publications