Scientific Computing Group Seminars - Detail View

Speaker: D Fishelov

Affiliation: Afeka and Tel Aviv Universities

Talk Title: A High Order Compact Scheme for the Pure-Streamfunction Formulation of the Navier-Stokes Equations

Invited by: David Gottlieb

Time: Oct. 03 2008 11 a.m.

Location: 182 George Street, Room 110

Abstract:

We introduce a second order compact scheme for the streamfunction formulation, which is enhanced to a fourth-order scheme. We construct fourth order approximations for the Laplacian, the biharmonic and the nonlinear convective operators. The scheme is compact (nine-point stencil) for the Laplacian and the biharmonic operators, which are both treated implicitly in the time-stepping scheme. The approximation of the convective term, which is treated explicitly in the time-stepping scheme, is nearly compact (thirteen points stencil). However, no ghost points or artificial boundary conditions are needed for our scheme. We prove stability and convergence properties of these schemes. Numerical results demonstrate that the fourth order accuracy is actually obtained for several test-cases.