METHOD OF VARIATIONAL IMBEDDING FOR THE INVERSE PROBLEM OF BOUNDARY-LAYER THICKNESS IDENTIFICATION

The inverse problem of identification of boundary-layer thickness is r eplaced by the higher-order boundary value problem for the Euler-Lagra nge equations for minimization of the quadratic functional of the orig inal system (Method of Variational Imbedding - MVI). The imbedding pro blem is correct in the sense of Hadamard and consists of an explicit d ifferential equation for the boundary-layer thickness. The existence a nd uniqueness of solution of the linearized imbedding problem is demon strated and a difference scheme of splitting type is proposed for its numerical solution. The performance of the technique is demonstrated f or three different boundary-layer problems: the Blasius problem, flow in the vicinity of plane stagnation point and the flow in the leading stagnation point on a circular cylinder. Comparisons with the self-sim ilar solutions where available are quantitatively very good.