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dc.contributor.authorDalcin, Lisandro
dc.contributor.authorRojas, Diego B.
dc.contributor.authorZampini, Stefano
dc.contributor.authorDel Rey Fernández, David C.
dc.contributor.authorCarpenter, Mark H.
dc.contributor.authorParsani, Matteo
dc.date.accessioned2019-08-18T13:45:47Z
dc.date.available2019-08-18T13:45:47Z
dc.date.issued2019-08-01
dc.identifier.citationDalcin, L., Rojas, D. B., Zampini, S., Del Rey Fernández, D. C., Carpenter, M. H., & Parsani, M. (2019). Conservative and entropy stable solid wall boundary conditions for the compressible Navier–Stokes equations: Adiabatic wall and heat entropy transfer. Journal of Computational Physics. doi:10.1016/j.jcp.2019.06.051
dc.identifier.doi10.1016/j.jcp.2019.06.051
dc.identifier.urihttp://hdl.handle.net/10754/656483
dc.description.abstractWe present a novel technique for the imposition of non-linear entropy conservative and entropy stable solid wall boundary conditions for the compressible Navier–Stokes equations in the presence of an adiabatic wall, or a wall with a prescribed heat entropy flow. The procedure relies on the formalism and mimetic properties of diagonal-norm, summation-by-parts and simultaneous-approximation-term operators, and is a generalization of previous works on discontinuous interface coupling [1] and solid wall boundary conditions [2]. Using the method of lines, a semi-discrete entropy estimate for the entire domain is obtained when the proposed numerical imposition of boundary conditions are coupled with an entropy-conservative or entropy-stable discrete interior operator. The resulting estimate mimics the global entropy estimate obtained at the continuous level. The boundary data at the wall are weakly imposed using a penalty flux approach and a simultaneous-approximation-term technique for both the conservative variables and the gradient of the entropy variables. Discontinuous spectral collocation operators (mass lumped nodal discontinuous Galerkin operators), on high-order unstructured grids, are used for the purpose of demonstrating the robustness and efficacy of the new procedure for weakly enforcing boundary conditions. Numerical simulations confirm the non-linear stability of the proposed technique, with applications to three-dimensional subsonic and supersonic flows. The procedure described is compatible with any diagonal-norm summation-by-parts spatial operator, including finite element, finite difference, finite volume, discontinuous Galerkin, and flux reconstruction schemes.
dc.description.sponsorshipThe research reported in this paper was funded by King Abdullah University of Science and Technology. We are thankful for the computing resources of the Supercomputing Laboratory and the Extreme Computing Research Center at King Abdullah University of Science and Technology.
dc.publisherElsevier BV
dc.relation.urlhttps://linkinghub.elsevier.com/retrieve/pii/S0021999119304590
dc.rightsNOTICE: this is the author’s version of a work that was accepted for publication in Journal of Computational Physics. 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 Journal of Computational Physics, [[Volume], [Issue], (2019-08-01)] DOI: 10.1016/j.jcp.2019.06.051 . © 2019. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
dc.subjectCompressible Navier–Stokes equations
dc.subjectSolid wall
dc.subjectEntropy conservation
dc.subjectEntropy stability
dc.subjectSummation-by-parts operators
dc.subjectSimultaneous-approximation-terms
dc.titleConservative and entropy stable solid wall boundary conditions for the compressible Navier–Stokes equations: Adiabatic wall and heat entropy transfer
dc.typeArticle
dc.contributor.departmentExtreme Computing Research Center
dc.contributor.departmentApplied Mathematics and Computational Science Program
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.identifier.journalJournal of Computational Physics
dc.rights.embargodate2021-08-01
dc.eprint.versionPost-print
dc.contributor.institutionNational Institute of Aerospace, Hampton, VA, United States
dc.contributor.institutionComputational AeroSciences Branch, NASA Langley Research Center, Hampton, VA, United States
kaust.personDalcin, Lisandro
kaust.personRojas, Diego B.
kaust.personZampini, Stefano
kaust.personParsani, Matteo
dc.date.published-online2019-08-01
dc.date.published-print2019-08


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