The Method of Matched Asymptotic Expansions and Its Generalizations

Abstract

Milton Van Dyke'sVan Dyke, M.Perturbation Methods in Fluid Mechanics [490]Perturbation Methods in Fluid Mechanicswas effectively both the earliest and the most influential book specifically about applied singular perturbations. (Some credit might be given earlier fluid dynamics textbooks, e.g., Hayes and Probstein [199]). Van Dyke extensively surveyed the large extant aeronautical and fluid dynamical literature, forcefully advocating and clarifying the so-called method of matched asymptotic (or inner and outer) expansionsmatched asymptotic expansionsouter expansion. Although Van Dyke acknowledged that Prandtl's boundary layer theory was the prototype singular perturbation problem, he introduced the subject by describing incompressible fluid flow past a thin airfoil. The book's highlight message, sometimes called Van Dyke's magic ruleVan Dyke, M.magic rule, states: