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An entropy stable, hybridizable discontinuous Galerkin method for the compressible Navier-Stokes equations


Author: D. M. Williams
Journal: Math. Comp. 87 (2018), 95-121
MSC (2010): Primary 65M12, 65M60, 76N99
DOI: https://doi.org/10.1090/mcom/3199
Published electronically: May 31, 2017
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Abstract: This article proves that a particular space-time, hybridizable discontinuous Galerkin method is entropy stable for the compressible Navier-Stokes equations. In order to facilitate the proof, `entropy variables' are utilized to rewrite the compressible Navier-Stokes equations in a symmetric form. The resulting form of the equations is discretized with a hybridizable discontinuous finite element approach in space, and a classical discontinuous finite element approach in time. Thereafter, the initial solution is shown to continually bound the solutions at later times.


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Additional Information

D. M. Williams
Affiliation: Computational Aerodynamic Optimization, Flight and Vehicle Technology, Boeing Research and Technology, P.O. Box 3707, MC OR-420, Seattle, Washington 98124
Address at time of publication: Department of Mechanical and Nuclear Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802
Email: david.m.williams@psu.edu

DOI: https://doi.org/10.1090/mcom/3199
Keywords: Hybridizable discontinuous Galerkin, space-time, entropy stability, compressible Navier-Stokes
Received by editor(s): April 30, 2015
Received by editor(s) in revised form: February 23, 2016, and September 7, 2016
Published electronically: May 31, 2017
Article copyright: © Copyright 2017 D. M. Williams, The Boeing Company

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