Velocity-Vorticity Simulation of Unsteady 3-D Viscous Flow within a Driven Cavity

Summary

A velocity-vorticity formulation of the unsteady three dimensional Navier-Stokes equations has been used to solve for the incompressible viscous flow within a driven cavity of spanwise aspect ratio 3:1 at a Reynolds number Re = 3200 on a non-uniform (65 × 65 × 49) grid covering one half of the span. An efficient Alternating-DirectionImplicit method which treats all cross derivative terms implicitly and which requires only six scalar tridiagonal sweeps has been developed for the vorticity transport equation. The divergence-curl formulation for the elliptic velocity problem is solved at each time step by a Multi-Grid Distributive Gauss-Seidel iterative scheme. The pressure is solved, only when desired, from the three-dimensional Pressure Poisson problem using a Multi-Grid Gauss-Seidel iterative scheme. Velocity, vorticity and pressure results are given for a characteristic time t = 50 after the upper surface of the cavity is impulsively started from rest.