HTR approach to the asymptotic solutions of supersonic boundary layer problem: the case of slow acoustic waves interacting with streamwise isolated wall roughness

We address supersonic boundary layer flow to slow acoustic waves using homotopy renormalization method. The model involves an ordinary equation system, which allows us to investigate the problem analytically and find asymptotic solutions in explicit form. At first, we rewrite the original problem in the form of a system of inhomogeneous variable coefficients homotopy equations and then handle them by the traditional perturbation theory, using renormalization group methods to eliminate the secular terms. We prove analytically and numerically the high accuracy of our solutions, and study in some details the effects of Mach number and wall temperature. Finally, we discuss how the explicit expression of boundary thickness makes our solutions suitable for practical applications. To the best of our knowledge, this is the first time that the HTR method is applied to supersonic boundary flow, and the analytic solutions are obtained. These solutions are easy to apply, and they could also help provide deeper insight into the supersonic boundary layer model.