Mass Conservation of the Unified Continuous and Discontinuous Element-Based Galerkin Methods on Dynamically Adaptive Grids with Application to Atmospheric Simulations
Abstract
We perform a comparison of mass conservation properties of the continuous (CG) and discontinuous (DG)
Galerkin methods on non-conforming, dynamically adaptive meshes for two atmospheric test cases. The
two methods are implemented in a unified way which allows for a direct comparison of the non-conforming
edge treatment. We outline the implementation details of the non-conforming direct stiffness summation
algorithm for the CG method and show that the mass conservation error is similar to the DG method. Both
methods conserve to machine precision, regardless of the presence of the non-conforming edges. For lower
order polynomials the CG method requires additional stabilization to run for very long simulation times.
We addressed this issue by using filters and/or additional artificial viscosity. The mathematical proof of
mass conservation for CG with non-conforming meshes is presented in Appendix B.
Description
The article of record as published may be located at http://dx.doi.org/10.1016/j.jcp.2015.05.010
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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