This paper develops a method of characteristics for supersonic viscous flows. The proposed method removes the inviscid and isentropic assumptions of the classical method of characteristics. The characteristic equations and compatibility equations are derived from the governing equations for compressible viscous flow. By combining the characteristic lines, the triangular interior unit process, quadrilateral interior unit process, and direct sonic point unit process are developed. The unit processes make up the characteristic net. The numerical algorithms consider the path of flow signal propagation. The inviscid terms are solved along characteristic lines, while the viscous terms are corrected through iterative whole-field computations. The proposed method has been applied to supersonic flat-plate boundary layer and verified by the similarity solution. The errors of velocity and temperature profiles are on the order of 0.1%, while the computation efficiency is the same as the classical method of characteristics. The accuracy and efficiency make the proposed method potential to become a basic tool of analysis and design for supersonic viscous flows.

Flowfield inverse design can obtain the desired flow and contour with high design efficiency, short design cycle, and small modification need. In this study, the Euler equations are formulated in the stream-function coordinates and combined with the given boundary conditions to derive a gridless space-marching method for the inverse design of subsonic, transonic, and supersonic flowfields. Designers can prescribe the flow parameters along the reference streamline to design flowfields and aerodynamic contours. The method is validated by the theoretical transonic solution, computational fluid dynamics, and experimental data, respectively. The method supports the fabrication of a Mach 2.0 single expansion tunnel. The calibration data agree well with the prescribed pressure distribution. The method is successfully applied to inverse design of contractions, nozzles, and asymmetric channels. Compared to classical analytic contractions, the contractions designed by the space-marching method provide a more accurate transonic flow. Compared to the classical Sivells’ nozzle, the nozzle designed by the space-marching method provides a smaller workload, a more flexible velocity distribution, a 20% reduction in length, and an equally uniform flow. Additionally, the space-marching method is applied to design the asymmetric channels under various Mach numbers. These asymmetric channels perfectly eliminate Mach waves, achieving the shock-free flow turning and high flow uniformity. These results validate the feasibility of the spacemarching method, making it a good candidate for the inverse design of subsonic, transonic, and supersonic internal flowfields and aerodynamic contours.