Development of a TwoDimensional/Axisymmetric implicit NavierStokes solver using fluxdifference splitting concepts and fully general geometry
Abstract
Theoretical background and several basic test cases are presented for a new, time dependent NavierStokes solver for twodimensional and axisymmetric flows. The goal of the effort is to invoke stateoftheart computational fluid dynamics (CFD) technology to improve modeling of viscous phenomenal and to increase the robustness of CFD analysis. The original motivation was inadequate representation of supersonic rampinduced separation by existing CFD codes. The present work addresses that inadequacy by using modern numerical methods which accurately model signal propagation in highspeed fluid flow. This technique solves the NavierStokes equations in general curvilinear coordinates in a foursided domain bounded by a wall, and upper boundary opposite the wall, an inflow boundary, and an outflow boundary. The interior algorithm is a fluxdifference splitting method similar to that of Yang, Lombard, and Bershader, but is blended into a second order, implicit factored delta form. With implicitly treated boundary conditions, the solution is performed using a block tridiagonal method followed by an explicit updating of the boundaries. The resulting scheme satisfies the global conversation requirement to within the order of accuracy of the algorithm. The grid is generated using a relaxation Poisson solver. A systematic and rigorous development of the complete method is presented. Initial steps in code validation include successful reproduction of Couette and Blasius solutions.
 Publication:

Final Report
 Pub Date:
 September 1985
 Bibcode:
 1985cals.reptR....H
 Keywords:

 Axisymmetric Flow;
 Computational Fluid Dynamics;
 NavierStokes Equation;
 Two Dimensional Flow;
 Accuracy;
 Algorithms;
 Boundaries;
 Boundary Conditions;
 Grid Generation (Mathematics);
 Models;
 Motivation;
 Numerical Analysis;
 Poisson Density Functions;
 Requirements;
 Signal Encoding;
 Spherical Coordinates;
 Technology Assessment;
 Time Dependence;
 Fluid Mechanics and Heat Transfer