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Boundary Layer Theory to Matched Asymptotics
Author(s) -
Ting L.
Publication year - 2000
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/1521-4001(200011)80:11/12<845::aid-zamm845>3.0.co;2-5
Subject(s) - singular perturbation , mathematics , boundary value problem , perturbation (astronomy) , mathematical analysis , boundary layer , mixed boundary condition , physics , mechanics , quantum mechanics
We describe the explanation of Prandtl's boundary layer theory by Friedrichs, leading to the boundary layer technique, or the method of matched asymptotics. The latter provides a systematic procedure for the formulation of a singular perturbation problem, the matching of local (inner) and global (outer) perturbation solutions, the identification of the “lost” boundary condition(s) from the full system of equations and the derivation of the higher order equations and their compatibility condition(s), if any, which would be the closure condition(s) of the leading order solutions. Examples using the method of matched asymptotics are presented to demonstrate the “lost” condition(s) and the closure condition(s) and to emphasize the physical intuition needed to formulate the perturbation problem, i.e., the choice of the scalings and the expansion schemes, the physical meaning of the inner solution, and its matching with the outer solution, etc.