We study bridging relations of supersonic aerodynamics in transitional regime by direct simulation Monte Carlo(DSMC).Flows around a cylinder and a blunt double-wedge in a wide range of Mach and Knudsen numbers are simulated.The erf-log bridging relation exhibits good accuracy in supersonic aerodynamics in rarefied transitional regime.It is helpful in predicting low supersonic aerodynamic coefficients of sub-orbital spacecrafts by bridging relations.

We extend the unified coordinate system proposed by Hui et al.to axisymmetric Euler equations.The form and hyperbolicity of axisymmetric Euler equations are discussed.Solution of 1-D Riemann problem solved by axisymmetric Euler equations after dimensional splitting is shown.Axisymmetric Euler equations are numerically solved using Godunov scheme with MUSCL update.Numerical results show advantages of unified coordinates.

The Cartesian grid method initially developed for computing inviscid flows is extended to viscous flow problems. In order to reduce the number of mesh points and to be compatible with the anisotropic nature of viscous flows, an anisotropic Cartesian grid method is proposed. The stability of a space-centered interior difference scheme and that of a finite-difference solid wall condition are studied for the Cartesian grid. It is found that the anisotropic Cartesian grid method can substantially reduce the number of grid points without jeopadizing the accuracy.