Abstract: A finite element algorithm is proposed for solving the direct- and inverse-problems of three-dimensional boundary layers. The algorithm is constructed based on a Galerkin discretization along the traversal direction across the boundary layer, and a subdomain discretization in conjunction with a bi-directonal marching procedure along the body surface. The present algorithm would yield an explicit form of the CFL condition by incorporating the isoparametric elements, and thus provide an assurance for fast-solving the problems of both modes. For the inverse mode, the displacement thicknesses are considered as a set of constrains, and are integrated into the finite element analog of the boundary layer equations via Lagrange multipliers. Several test cases are computed by the present technique, and the results show that the present technique do provide an economical as well as efficient tool for computing three-dimensional boundary layer flows.

Key words: finite element algorithm, boundary layer equations, separated flows