A gradient-robust well-balanced scheme for the compressible isothermal Stokes problem

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dc.contributor.authorAkbas, M.
dc.contributor.authorGallouet, T.
dc.contributor.authorGassmann, A.
dc.contributor.authorLinke, A.
dc.contributor.authorMerdon, C.
dc.date.accessioned2021-12-01T18:50:20Z
dc.date.available2021-12-01T18:50:20Z
dc.date.issued2020
dc.department[Belirlenecek]en_US
dc.description.abstractA novel notion for constructing a well-balanced scheme - a gradient-robust scheme - is introduced and a showcase application for the steady compressible, isothermal Stokes equations in a nearly-hydrostatic situation is presented. Gradient-robustness means that gradient fields in the momentum balance are well-balanced by the discrete pressure gradient - which is possible on arbitrary, unstructured grids. The scheme is asymptotic-preserving in the sense that it reduces for low Mach numbers to a recent inf-sup stable and pressure-robust discretization for the incompressible Stokes equations. The convergence of the coupled FEM-FVM scheme for the nonlinear, isothermal Stokes equations is proved by compactness arguments. Numerical examples illustrate the numerical analysis, and show that the novel approach can lead to a dramatically increased accuracy in nearly-hydrostatic low Mach number flows. Numerical examples also suggest that a straightforward extension to barotropic situations with nonlinear equations of state is feasible. (C) 2020 Elsevier B.V. All rights reserved.en_US
dc.description.sponsorshipDAAD (German Academic Exchange Service) scholarshipDeutscher Akademischer Austausch Dienst (DAAD)en_US
dc.description.sponsorshipThis work has been partially funded by a DAAD (German Academic Exchange Service) scholarship, which supported a research stay of Mine Akbas at the Weierstrass Institute in Berlin in the period January to September 2018.en_US
dc.identifier.doi10.1016/j.cma.2020.113069
dc.identifier.issn0045-7825
dc.identifier.issn1879-2138
dc.identifier.scopus2-s2.0-85084672473en_US
dc.identifier.scopusqualityQ1en_US
dc.identifier.urihttps://doi.org/10.1016/j.cma.2020.113069
dc.identifier.urihttps://hdl.handle.net/20.500.12684/10862
dc.identifier.volume367en_US
dc.identifier.wosWOS:000562023900009en_US
dc.identifier.wosqualityQ1en_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakScopusen_US
dc.language.isoenen_US
dc.publisherElsevier Science Saen_US
dc.relation.ispartofComputer Methods In Applied Mechanics And Engineeringen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.subjectCompressible barotropic Stokes problemen_US
dc.subjectWell-balanced schemeen_US
dc.subjectGradient-robustnessen_US
dc.subjectFinite elementsen_US
dc.subjectFinite volumesen_US
dc.subjectFinite-Element Methodsen_US
dc.subjectDiscontinuous Galerkin Methodsen_US
dc.subjectVolume Schemeen_US
dc.subjectMixed Methodsen_US
dc.subjectEquationsen_US
dc.subjectErrorsen_US
dc.subjectOrderen_US
dc.subjectReconstructionen_US
dc.subjectModelsen_US
dc.titleA gradient-robust well-balanced scheme for the compressible isothermal Stokes problemen_US
dc.typeArticleen_US

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