Topology and Grid Adaption for High-Speed Flow Computations

This study investigates the effects of grid topology and grid adaption on numerical solutions of the Navier-Stokes equations. In the first part of this study, a general procedure is presented for computation of high-speed flow over complex three-dimensional configurations. This includes the grid generation and solution algorithm for Navier-Stokes equations in a general three-dimensional curvilinear coordinate system. The flow field is simulated on the surface of a Butler wing in a uniform stream. Results are presented for Mach number 3.5 and a Reynolds number of 2,000,000. The O-type and H-type grids have been used for this study, and the results are compared together and with other theoretical and experimental results. The results demonstrate that while the H-type grid is suitable for the leading and trailing edges, a more accurate solution can be obtained for the middle part of the wing with an O-type grid. In spite of some discrepancies, the present numerical results compare favorably with the experimental results. In the second part of this study, methods of grid adaption are reviewed and a method is developed with the capability of adapting to several variables. This method is based on a variational approach and is an algebraic method. Also, the method has been formulated in such a way that there is no need for any matrix inversion. This method is used in conjunction with the calculation of hypersonic flow over a blunt-nose body. A movie has been produced which shows simultaneously the transient behavior of the solution and the grid adaption. For both cases, the simulations are done by integrating the viscous Navier-Stokes equations. These equations govern the unsteady, viscous, compressible and heat-conducting flow of an ideal gas, and all viscous terms are retained. The equations are written in curvilinear coordinates so that the body surface is represented accurately. The computer codes are written in FORTRAN, is vectorized and currently run on the CDC Vector Processing System (VPS-32, CYBER 205) computer. The results indicate the viability and validity of the proposed methods