Journal
JOURNAL OF COMPUTATIONAL PHYSICS
Volume 297, Issue -, Pages 90-103Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2015.05.010
Keywords
Adaptive mesh refinement; Continuous Galerkin method; Discontinuous Galerkin method; Non-conforming mesh; Compressible Euler equations; Atmospheric simulations
Funding
- Office of Naval Research [PE-0602435N]
- National Science Foundation (Division of Mathematical Sciences) [121670]
- Air Force Office of Scientific Research through the Computational Mathematics program
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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. (C) 2015 Elsevier Inc. All rights reserved.
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