Solution of the incompressible driven cavity problem by the alternating-direction implicit method

摘要

A second-order accurate alternating-direction implicit (ADI) method was used to solve the two-dimensional incompressible Navier-Stokes equations for flow in a square driven cavity. Calculations were made at a Reynolds number of 100 with equally spaced 15 by 15, 17 by 17, 33 by 33, and 57 by 57 grids and at a Reynolds number of 10 with a 15 by 15 grid. The ADI results agree well with other solutions. Choosing a criterion for convergence which was too strict was found to result in no steady-state solution being reached. A study of the maximum allowable time step for a Reynolds number of 100 indicated that time steps many times larger than those used for most consistent explicit methods could be used for the ADI method. Tables (data) of flow velocity and stream functions are given.