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Entropy Stable Staggered Grid Spectral Collocation for the Burgers' and Compressible Navier-Stokes Equations Staggered grid, entropy stable discontinuous spectral collocation operators of any order are developed for Burgers' and the compressible Navier-Stokes equations on unstructured hexahedral elements. This generalization of previous entropy stable spectral collocation work [1, 2], extends the applicable set of points from tensor product, Legendre-Gauss-Lobatto (LGL) to a combination of tensor product Legendre-Gauss (LG) and LGL points. The new semi-discrete operators discretely conserve mass, momentum, energy and satisfy a mathematical entropy inequality for both Burgers' and the compressible Navier-Stokes equations in three spatial dimensions. They are valid for smooth as well as discontinuous flows. The staggered LG and conventional LGL point formulations are compared on several challenging test problems. The staggered LG operators are significantly more accurate, although more costly to implement. The LG and LGL operators exhibit similar robustness, as is demonstrated using test problems known to be problematic for operators that lack a nonlinearly stability proof for the compressible Navier-Stokes equations (e.g., discontinuous Galerkin, spectral difference, or flux reconstruction operators).
Document ID
20160001635
Acquisition Source
Langley Research Center
Document Type
Technical Memorandum (TM)
Authors
Carpenter, Mark H. (NASA Langley Research Center Hampton, VA, United States)
Parsani, Matteo (NASA Langley Research Center Hampton, VA, United States)
Fisher, Travis C. (Sandia National Labs. Albuquerque, NM, United States)
Nielsen, Eric J. (NASA Langley Research Center Hampton, VA, United States)
Date Acquired
February 5, 2016
Publication Date
December 1, 2015
Subject Category
Numerical Analysis
Report/Patent Number
NF1676L-22150
NASA/TM-2015-218990
L-20597
Funding Number(s)
WBS: WBS 794072.02.07.02.03
Distribution Limits
Public
Copyright
Public Use Permitted.

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