Numerical solution of the NavierStokes equations for laminar, transonic flows
Abstract
An implicit finite difference solution of the NavierStokes equations yielded time histories of the transonic laminar flow development about a circular cylinder and NACA0018 airfoil. Reynolds numbers ranged from those corresponding to purely laminar flow to those corresponding to significant turbulence in the boundary layer. Body thermal conditions of an adiabatic wall and a specified body temperature were considered. Versatility in treating arbitrary bodies was incorporated by using numerically generated, bodyfitted coordinate transformations. Solution of the simultaneous difference equations for the dependent variables was obtained using an accelerated GaussSeidel iterative scheme. Computational results are presented in the form of velocity vector fields, Mach number contours, aerodynamic coefficients, heat transfer rates at the body surface, and body temperature distributions. Truncation analyses of first and second derivative difference approximations resulted in general criteria for numerically generated coordinates so that flow near a body is more accurately represented.
 Publication:

Ph.D. Thesis
 Pub Date:
 May 1979
 Bibcode:
 1979PhDT........31T
 Keywords:

 Finite Difference Theory;
 Laminar Flow;
 NavierStokes Equation;
 Transonic Flow;
 Aerodynamic Coefficients;
 Airfoils;
 Circular Cylinders;
 Heat Flux;
 Iterative Solution;
 Mach Number;
 Reynolds Number;
 Temperature Distribution;
 Two Dimensional Bodies;
 Velocity Distribution;
 Fluid Mechanics and Heat Transfer