A pure-compact scheme for the streamfunction formulation of Navier-Stokes equations

Authors:
Matania Ben-Artzi;Jean-Pierre Croisille;Dalia Fishelov;Shlomo Trachtenberg
Affiliations:
Institute of Mathematics, The Hebrew University, Jerusalem 91904, Israel;Department of Mathematics, University of Metz, Metz, France;Tel-Aviv Academic College of Engineering, 218 Bnei-Efraim St., Tel-Aviv 69107, Israel and School of Mathematical Sciences, Tel Aviv University, Ramat Aviv, Tel Aviv 69978, Israel;Department of Membrane and Ultrastructure Research, The Hebrew University-Hadassah Medical School, P.O. Box 12271, Jerusalem 91120, Israel
Venue:
Journal of Computational Physics
Year:
2005

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Abstract

A pure-streamfunction formulation is introduced for the numerical simulation of the two-dimensional incompressible Navier-Stokes equations. The idea is to replace the vorticity in the vorticity-streamfunction evolution equation by the Laplacian of the streamfunction. The resulting formulation includes the streamfunction only, thus no inter-function relations need to be invoked. A compact numerical scheme, which interpolates streamfunction values as well as its first order derivatives, is presented and analyzed. A number of numerical experiments are presented, including driven and double driven cavities, where the Reynolds numbers are sufficiently large, leading to symmetry breaking of asymptotic solutions.