Del Rey Fernandez, David C., Carpenter, Mark H., Dalcin, Lisandro, Friedrich, Lucas, Winters, Andrew R., Gassner, Gregor J. and Parsani, Matteo (2020). Entropy Stable p-Nonconforming Discretizations with the Summation-by-Parts Property for the Compressible Navier-Stokes Equations. Technical Report.


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The entropy conservative, curvilinear, nonconforming, p-refinement algorithm for hyperbolic conservation laws of Del Rey Fernández et al. (2019), is extended from the compressible Euler equations to the compressible Navier–Stokes equations. A simple and flexible coupling procedure with planar interpolation operators between adjoining nonconforming elements is used. Curvilinear volume metric terms are numerically approximated via a minimization procedure and satisfy the discrete geometric conservation law conditions. Distinct curvilinear surface metrics are used on the adjoining interfaces to construct the interface coupling terms, thereby localizing the discrete geometric conservation law constraints to each individual element. The resulting scheme is entropy conservative/stable, element-wise conservative, and freestream preserving. Viscous interface dissipation operators are developed that retain the entropy stability of the base scheme. The accuracy and stability properties of the resulting numerical scheme are shown to be comparable to those of the original conforming scheme (achieving ∼ p + 1 convergence) in the context of the viscous shock problem, the Taylor–Green vortex problem at a Reynolds number of Re = 1,600, and a subsonic turbulent flow past a sphere at Re = 2,000.

Item Type: Preprints, Working Papers or Reports (Technical Report)
CreatorsEmailORCIDORCID Put Code
Del Rey Fernandez, David C.dcdelrey@gmail.comUNSPECIFIEDUNSPECIFIED
Carpenter, Mark H.mark.h.carpenter@nasa.govUNSPECIFIEDUNSPECIFIED
Dalcin, Lisandrodalcinl@gmail.comUNSPECIFIEDUNSPECIFIED
Friedrich, Lucaslfriedri@math.uni-koeln.deUNSPECIFIEDUNSPECIFIED
Winters, Andrew R.andrew.ross.winters@liu.seUNSPECIFIEDUNSPECIFIED
Gassner, Gregor J.ggassner@math.uni-koeln.deUNSPECIFIEDUNSPECIFIED
URN: urn:nbn:de:hbz:38-115230
Series Name at the University of Cologne: Technical report series. Center for Data and Simulation Science
Volume: 2020,2
Date: 20 July 2020
Language: English
Faculty: Central Institutions / Interdisciplinary Research Centers
Divisions: Weitere Institute, Arbeits- und Forschungsgruppen > Center for Data and Simulation Science (CDS)
Subjects: Natural sciences and mathematics
Technology (Applied sciences)
Uncontrolled Keywords:
compressible Navier–Stokes equationsEnglish
nonconforming interfacesEnglish
nonlinear entropy stabilityEnglish
summation-by-parts and simultaneous-approximation-termsEnglish
curved elementsEnglish
unstructured gridsEnglish


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