TWO-LEVEL METHOD FOR UNSTEADY NAVIER-STOKES EQUATIONS IN STREAM FUNCTION FORM

摘要

Two-level finite element approximation to stream function form of unsteady Navier-Stokes equations is studied. This algorithm involves solving one nonlinear system on a coarse grid and one linear problem on a fine grid. Moreover, the scaling between these two grid sizes is super-linear. Approximation, stability and convergence aspects of a fully discrete scheme are analyzed. At last a numrical example is given whose results show that the algorithm proposed in this paper is effcient.