DEVELOPMENT AND APPLICATION OF AN INTEGRAL METHOD FOR THE INCOMPRESSIBLE NAVIER-STOKES EQUATIONS

A new integral approach to solving linear elliptic equations was first developed and then applied to the nonlinear incompressible Navier-Stokes(NS) equations. For the NS equations the Direct, Formal Integration (DFI) method was applied to calculate the velocity and pressure, in a rectangular channel and in a driven cavity. For the calculation of pressure, three techniques were incorporated into the DFI scheme. Abdallah's method for calculating the pressure, with DFI, was computationally most efficient for the channel flow problem. For the driven cavity experiment, DFI with "SIMPLE" was the best. In all cases, the divergence-free constraint served as a check and convergence criteria.