Approximations of the Navier–Stokes equations for high Reynolds number flows past a solid wall

• Published in: Journal of computational and applied mathematics 2004-04, Vol.166 (1), p.101-122
• Main Authors: Cousteix, J., Mauss, J.
• Format: Article
• Language: English
• Subjects: Asymptotic expansions; Boundary layer; Exact sciences and technology; External vorticity effects; High Reynolds number flow; Higher order effects in boundary layers; Mathematical analysis; Mathematics; Numerical analysis; Numerical analysis. Scientific computation; Partial differential equations; Partial differential equations, boundary value problems; Sciences and techniques of general use; Singular perturbations
• ISSN: 0377-0427; 1879-1778
• DOI: 10.1016/j.cam.2003.09.035

Approximations of the Navier–Stokes equations at high Reynolds number near solid boundaries are studied by using a method of successive complementary expansions. The starting point of the method is to look for a uniformly valid nonregular approximation. No matching principle is required to construct the approximation. The application of this method leads rigorously to the theory of interactive boundary layer which relies upon generalized boundary layer equations strongly coupled to the inviscid equations for the outer stream. It is shown that the interactive boundary layer model contains the Prandtl boundary layer model and the triple deck model. These two models are two different regular expansions of the interactive boundary layer which are deduced asymptotically, i.e., when the Reynolds number goes to infinity. Applications of the interactive boundary layer model to boundary layers influenced by external vorticity are presented and compared with Navier–Stokes solutions.