Three-dimensional viscous flow solutions with a vorticity-stream function formulation

Abstract

Abstract : A three-dimensional streamlike function/vorticity transport procedure has been developed to analyze two- and three-dimensional inviscid and viscous flows. Both the formulation and the numerical techniques used to solve these equations contain many of the advantages of interacting boundary layer theory for strongly interacting viscous and inviscid flows. An algorithm which involves the solution of two uncoupled Poisson/vorticity transport equation sets is described. An implicit line relaxation scheme is used to solve a 2 x 2 block-tridiagonal system for the Poisson and vorticity transport equations in each of the x- and z-directions. Solutions for 2-D and 3-D inviscid and viscous flows are compared with other numerical solutions demonstrating the stability and accuracy of the current procedure. Favorable agreement with the recently obtained 3-D interacting boundary layer solutions of Edwards demonstrates the overall accuracy of this new approach for 3-D viscous flows including flow separation. This streamlike function/vorticity transport procedure has been found to yield smooth solutions without the need to add explicit artificial viscosity. Keywords: stream function; finite difference coefficients; Navier Stokes equations.