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

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. T...

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Bibliographic Details
Published in:Journal of computational physics 2016-05, Vol.312, p.175-191
Main Authors: Mohamed, Mamdouh S., Hirani, Anil N., Samtaney, Ravi
Format: Article
Language:English
Subjects:
Accuracy
Calculus
Covolume method
Discrete exterior calculus (DEC)
Discretization
Exteriors
Incompressible flow
Mathematical analysis
Mathematical models
Navier-Stokes equations
Navier–Stokes
Operators (mathematics)
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Summary: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.
ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2016.02.028