Discrete exterior calculus discretization of incompressible Navier–Stokes equations over surface simplicial meshes

Handle URI:
http://hdl.handle.net/10754/596175
Title:
Discrete exterior calculus discretization of incompressible Navier–Stokes equations over surface simplicial meshes
Authors:
Mohamed, Mamdouh S.; Hirani, Anil N. ( 0000-0003-3506-1703 ) ; Samtaney, Ravi ( 0000-0002-4702-6473 )
Abstract:
A conservative discretization of incompressible Navier–Stokes equations is developed based on discrete exterior calculus (DEC). A distinguishing feature of our method is the use of an algebraic discretization of the interior product operator and a combinatorial discretization of the wedge product. The governing equations are first rewritten using the exterior calculus notation, replacing vector calculus differential operators by the exterior derivative, Hodge star and wedge product operators. The discretization is then carried out by substituting with the corresponding discrete operators based on the DEC framework. Numerical experiments for flows over surfaces reveal a second order accuracy for the developed scheme when using structured-triangular meshes, and first order accuracy for otherwise unstructured meshes. By construction, the method is conservative in that both mass and vorticity are conserved up to machine precision. The relative error in kinetic energy for inviscid flow test cases converges in a second order fashion with both the mesh size and the time step.
KAUST Department:
Mechanical Engineering Program; Physical Sciences and Engineering (PSE) Division
Citation:
Discrete exterior calculus discretization of incompressible Navier–Stokes equations over surface simplicial meshes 2016 Journal of Computational Physics
Publisher:
Elsevier BV
Journal:
Journal of Computational Physics
Issue Date:
11-Feb-2016
DOI:
10.1016/j.jcp.2016.02.028
Type:
Article
ISSN:
00219991
Additional Links:
http://linkinghub.elsevier.com/retrieve/pii/S0021999116000929
Appears in Collections:
Articles; Physical Sciences and Engineering (PSE) Division; Mechanical Engineering Program

Full metadata record

DC FieldValue Language
dc.contributor.authorMohamed, Mamdouh S.en
dc.contributor.authorHirani, Anil N.en
dc.contributor.authorSamtaney, Ravien
dc.date.accessioned2016-02-14T14:09:52Zen
dc.date.available2016-02-14T14:09:52Zen
dc.date.issued2016-02-11en
dc.identifier.citationDiscrete exterior calculus discretization of incompressible Navier–Stokes equations over surface simplicial meshes 2016 Journal of Computational Physicsen
dc.identifier.issn00219991en
dc.identifier.doi10.1016/j.jcp.2016.02.028en
dc.identifier.urihttp://hdl.handle.net/10754/596175en
dc.description.abstractA conservative discretization of incompressible Navier–Stokes equations is developed based on discrete exterior calculus (DEC). A distinguishing feature of our method is the use of an algebraic discretization of the interior product operator and a combinatorial discretization of the wedge product. The governing equations are first rewritten using the exterior calculus notation, replacing vector calculus differential operators by the exterior derivative, Hodge star and wedge product operators. The discretization is then carried out by substituting with the corresponding discrete operators based on the DEC framework. Numerical experiments for flows over surfaces reveal a second order accuracy for the developed scheme when using structured-triangular meshes, and first order accuracy for otherwise unstructured meshes. By construction, the method is conservative in that both mass and vorticity are conserved up to machine precision. The relative error in kinetic energy for inviscid flow test cases converges in a second order fashion with both the mesh size and the time step.en
dc.language.isoenen
dc.publisherElsevier BVen
dc.relation.urlhttp://linkinghub.elsevier.com/retrieve/pii/S0021999116000929en
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, 11 February 2016. DOI: 10.1016/j.jcp.2016.02.028en
dc.subjectDiscrete exterior calculus (DEC)en
dc.subjectNavier–Stokesen
dc.subjectIncompressible flowen
dc.subjectCovolume methoden
dc.titleDiscrete exterior calculus discretization of incompressible Navier–Stokes equations over surface simplicial meshesen
dc.typeArticleen
dc.contributor.departmentMechanical Engineering Programen
dc.contributor.departmentPhysical Sciences and Engineering (PSE) Divisionen
dc.identifier.journalJournal of Computational Physicsen
dc.eprint.versionPost-printen
dc.contributor.institutionDepartment of Mathematics, University of Illinois at Urbana–Champaign, IL, USAen
dc.contributor.affiliationKing Abdullah University of Science and Technology (KAUST)en
kaust.authorMohamed, Mamdouh S.en
kaust.authorSamtaney, Ravien
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