Abstract

We present a framework for computing flows on surfaces based on a discrete exterior calculus (DEC) discretization of Navier-Stokes (N-S) equations on simplicial meshes. The framework incorporates primitive formulation of the N-S equations and allows for a time integration method which features energy conservation [1]. Other features of the framework consist of the inclusion of the Coriolis force term to investigate flows on rotating surfaces, and an interface tracking method for multiphase flows. The method is second order accurate on structured triangular meshes, and first order on otherwise unstructured meshes, and demonstrates the conservation of inviscid invariants such as kinetic energy and enstrophy over an extended period of time [2].