Uniformly valid approximation for singular perturbation problems and matching principle
Jacques Mauss, J. Cousteix · Comptes Rendus Mécanique · 2002
After a brief reminder of the notion of asymptotic expansion, a counter-example of the Van Dyke matching principle is solved thanks to a modified form of this principle. This leads to a composite approximation to a given order. The proposed method of successive complementary expansions reverses the analysis by starting with a supposed form of the uniformly valid approximation. This method does not require any matching principle which, in fact, is a by-product. The method is illustrated with the very often studied one-dimensional model of Stokes–Oseen for the circular cylinder.