Unsteady three-dimensional flow simulation using vorticity-velocity form of Navier-Stokes equations and ADI+MG-DGS method

An approach is designed for simulating three-dimensional incompressible flow fields using the time-dependent Navier-Stokes equations in terms of vorticity-velocity variables. An alternating-direction-implicit (ADI) method is developed and used to solve the vorticity-transport equation, and a distributive Gauss-Seidel (DGS) scheme, together with a multigrid technique for convergence acceleration, is used to effectively relax the system of equations for the velocity problem. It is shown that the overall numerical ADI method including the multigrid DSG algorithm is able to efficiently and robustly solve the Navier-Stokes equations formulated in the vorticity-velocity variables for unsteady three-dimensional incompressible flows.