In this thesis, numerical schemes to solve the viscous hypersonic flow over a blunt body are discussed and a robust modification of the split Mach numbers of low-diffusion flux-splitting scheme (LDFSS) is proposed. The modification is focused on the cure of nonmonotone behavior of the original LDFSS(0) in the vicinity of shock wave. Computational results indicate that the present modification ensures monotone shock capturing without deteriorating the accuracy in the viscous region. The time implicit point symmetric Gauss-Seidel scheme (point SGS) is applied to compute hypersonic viscous flows in thermochemical nonequilibrium. The performance of the point SGS scheme is then compared with those of the line SGS and the LU-SGS schemes. Results indicate that the point SGS scheme with multiple sweeps is as robust and efficient as the line SGS scheme.
By using the Navier-Stokes code based on the proposed modification, nonequilibrium hypersonic flows past small radius spherical bodies with emphasis on stagnation heating are investigated. To validate the accuracy of the present Navier-Stokes code, computations are performed for several problems and results are compared with those by VSL or DSMC method. By coupling the Navier-Stokes code with the DOT/DOC optimization code, velocity-altitude map is constructed under the constraint of upper limit wall temperature for a spherical body of radius 0.01m at altitudes from 30km to 70km. When the present velocity-altitude map is compared with that obtained by the engineering correlation approach where the Fay and Riddell theory and Rankine-Hugoniot relation are utilized, it is found that the maximum allowable velocity of the present computation is much smaller than that predicted by the engineering correlation. The computational results of the Navier-Stokes code indicate that the thermochemical state of the flowfield and properties of the shock wave and boundary layer are quite different from those usually assumed in the engineering correlation approach.
