APPLICATION OF THE PIECEWISE PARABOLIC FINITE ANALYTIC METHOD TO THE 3-DIMENSIONAL CAVITY FLOW

The three-dimensional piecewise parabolic finite analytic method (PPFA M3D) with vector potential and vorticity as dependent variables, was u sed to solve the steady three-dimensional (3-D) laminar cavity flow. P redictions were obtained for Reynolds numbers between 100 and 2000. Re sults far Re = 100, 400, and 1000 are compared with those available in the literature. The overall agreement is excellent. Results are also compared with the two-dimensional PPFAM cavity flow, showing the effec t of three-dimensionality on the velocity predictions at the symmetry plane. The PPFAM3D is a robust numerical algorithm requiring no relaxa tion fo produce physically meaningful and numerically converged soluti ons. If is a promising tool for solving a variety of flow phenomena go verned by unsteady second-order partial differential convection-diffus ion equations.