Analytical methodologies for hypersonic propulsion

In this study, we review several analytical frameworks that may be used in the context of high speed propulsion. To this end, inviscid and boundary layer models are examined in the light of modern mathematical techniques. A modified Rayleigh-Janzen approach is offered as a possible improvement over previous inviscid techniques for handling hypersonic flow problems. The Successive Complementary Expansions Method (SCEM) is also examined as a general perturbation technique with application to the hypersonic boundary layer equations. Furthermore, the Homotopy Analysis Method (HAM) is introduced as a powerful yet seemingly overlooked approach for solving highly nonlinear problems. The HAM framework has been successfully employed over a wide range of topics ranging from fluid mechanics to finance. The strengths and weaknesses of these analytical methods are discussed to the extent of providing the reader with a roadmap directed toward their effective use.