A fully vectorized numerical solution of the incompressible NavierStokes equations
Abstract
A vectorizable algorithm is presented for the implicit finite difference solution of the incompressible NavierStokes equations in general curvilinear coordinates. The unsteady Reynolds averaged NavierStokes equations solved are in two dimension and nonconservative primitive variable form. A twolayer algebraic eddy viscosity turbulence model is used to incorporate the effects of turbulence. Two momentum equations and a Poisson pressure equation, which is obtained by taking the divergence of the momentum equations and satisfying the continuity equation, are solved simultaneously at each time step. An elliptic grid generation approach is used to generate a boundary conforming coordinate system about an airfoil. The governing equations are expressed in terms of the curvilinear coordinates and are solved on a uniform rectangular computational domain. A checkerboard SOR, which can effectively utilize the computer architectural concept of vector processing, is used for iterative solution of the governing equations.
 Publication:

Ph.D. Thesis
 Pub Date:
 December 1983
 Bibcode:
 1983PhDT........24P
 Keywords:

 Airfoils;
 Eddy Viscosity;
 Finite Difference Theory;
 NavierStokes Equation;
 Turbulent Flow;
 Architecture (Computers);
 Flow Distribution;
 Grid Generation (Mathematics);
 Iterative Solution;
 Poisson Equation;
 Turbulence Models;
 Vector Analysis;
 Velocity Distribution;
 Fluid Mechanics and Heat Transfer