"Discrete Exterior Calculus Discretization of Navier-Stokes Equations on Surface Meshes"

Dear All,

Mathematical Soft Matter Unit (Fried Unit) would like to invite you to a Seminar by Professor Anil Hirani from University of Illinois at Urbana-Champaign.

Date: Wednesday, February 24th, 2016
Time: 14:00-15:00
Venue: C016, LevelC, Lab 1
 

Speaker:
Professor Anil Hirani
Associate Professor
Department of Mathematics
University of Illinois at Urbana-Champaign

Title:
Discrete Exterior Calculus Discretization of Navier-Stokes Equations on Surface Meshes

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.  This is joint work with Mamdouh Mohamed and Ravi Samtaney of KAUST.