TY - JOUR

T1 - Discrete exterior calculus discretization of incompressible Navier–Stokes equations over surface simplicial meshes

AU - Mohamed, Mamdouh S.

AU - Hirani, Anil N.

AU - Samtaney, Ravi

N1 - KAUST Repository Item: Exported on 2020-10-01

PY - 2016/2/11

Y1 - 2016/2/11

N2 - 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.

AB - 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.

UR - http://hdl.handle.net/10754/596175

UR - http://linkinghub.elsevier.com/retrieve/pii/S0021999116000929

UR - http://www.scopus.com/inward/record.url?scp=84959359127&partnerID=8YFLogxK

U2 - 10.1016/j.jcp.2016.02.028

DO - 10.1016/j.jcp.2016.02.028

M3 - Article

VL - 312

SP - 175

EP - 191

JO - Journal of Computational Physics

JF - Journal of Computational Physics

SN - 0021-9991

ER -