Laminar Flow Over a Backward Facing Step — Finite-Difference Solution with Fast Fourier Transform for Regions Consisting of Rectangular Subdomains

Abstract

For the numerical solution of the Navier-Stokes equations fast direct solvers have been used in recent years for solving the Poisson equation for the stream function. However, in most cases the vorticity equation has been solved by iterative methods. If the Navier-Stokes equations in terms of stream function and vorticity are considered as a set of Poisson equations with Dirichlet boundary conditions it is then possible to make use of efficient Poisson solvers [1]. Here the Fast Fourier Transform procedure of Hockney [2] is applied to solve the flow over a backward facing step. This method has been successfully used for the prediction of the flow of microorganisms between floors of a multistoried hospital [3].