Threedimensional viscous flow solutions with a vorticitystream function formulation
Abstract
A threedimensional streamlike function/vorticity transport procedure has been developed to analyze two and threedimensional 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 blocktridiagonal system for the Poisson and vorticity transport equations in each of the x and zdirections. Solutions for 2D and 3D 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 3D interacting boundary layer solutions of Edwards demonstrates the overall accuracy of this new approach for 3D 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.
 Publication:

NASA STI/Recon Technical Report N
 Pub Date:
 May 1986
 Bibcode:
 1986STIN...8719653D
 Keywords:

 Boundary Layer Equations;
 Boundary Layer Separation;
 Flow Theory;
 Inviscid Flow;
 NavierStokes Equation;
 Poisson Equation;
 Viscous Flow;
 Vortices;
 Finite Difference Theory;
 Flow Coefficients;
 Three Dimensional Flow;
 Transport Properties;
 Two Dimensional Flow;
 Fluid Mechanics and Heat Transfer