A method of characteristics for supersonic viscous flows

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.