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dc.contributor.authorFernández, David C.Del Rey
dc.contributor.authorCarpenter, Mark H.
dc.contributor.authorDalcin, Lisandro
dc.contributor.authorFredrich, Lucas
dc.contributor.authorWinters, Andrew R.
dc.contributor.authorGassner, Gregor J.
dc.contributor.authorParsani, Matteo
dc.identifier.citationFernández, D. C. D. R., Carpenter, M. H., Dalcin, L., Fredrich, L., Winters, A. R., Gassner, G. J., & Parsani, M. (2020). Entropy-stable p-nonconforming discretizations with the summation-by-parts property for the compressible Navier–Stokes equations. Computers & Fluids, 210, 104631. doi:10.1016/j.compfluid.2020.104631
dc.description.abstractThe entropy-conservative/stable, 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 that retain the entropy stability of the base scheme are developed. The accuracy and stability of the resulting numerical scheme are shown to be comparable to those of the original conforming scheme in Carpenter et al. (2014) and Parsani et al. (2016), i.e., this scheme achieves ∼p+1/2 convergence on geometrically high-order distorted element grids; this is demonstrated 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.
dc.description.sponsorshipSpecial thanks are extended to Dr. Mujeeb R. Malik for partially funding this work as part of NASA's “Transformational Tools and Technologies” (T3) project. The research reported in this publication was also supported by funds from King Abdullah University of Science and Technology (KAUST). We are thankful for the computing resources of the Supercomputing Laboratory and the Extreme Computing Research Center at KAUST. Gregor Gassner and Lucas Friedrich were supported by the European Research Council (ERC) under the European Union's Eights Framework Program Horizon 2020 with the research project Extreme, ERC grant agreement no. 714487.
dc.publisherElsevier BV
dc.rightsNOTICE: this is the author’s version of a work that was accepted for publication in Computers and Fluids. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Computers and Fluids, [210, , (2020-06-23)] DOI: 10.1016/j.compfluid.2020.104631 . © 2020. This manuscript version is made available under the CC-BY-NC-ND 4.0 license
dc.titleEntropy-stable p-nonconforming discretizations with the summation-by-parts property for the compressible Navier–Stokes equations
dc.contributor.departmentExtreme Computing Research Center
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.contributor.departmentApplied Mathematics and Computational Science Program
dc.identifier.journalComputers and Fluids
dc.contributor.institutionNational Institute of Aerospace, Hampton, Virginia, United States
dc.contributor.institutionComputational AeroSciences Branch, NASA Langley Research Center, Hampton, Virginia, United States
dc.contributor.institutionMathematical Institute, University of Cologne, North Rhine-Westphalia, Germany
dc.contributor.institutionDepartment of Mathematics (MAI), Linköping University, Sweden
dc.contributor.affiliationKing Abdullah University of Science and Technology (KAUST)
kaust.personDalcin, Lisandro
kaust.personParsani, Matteo
kaust.acknowledged.supportUnitExtreme Computing Research Center
kaust.acknowledged.supportUnitSupercomputing Laboratory

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