ON THE CONVERGENCE AND EXACTNESS OF SOLUTIONS OF THE LAMINAR BOUNDARY-LAYER EQUATIONS USING THE N-PARAMETER INTEGRAL FORMULATION OF GALERKIN-KANTOROVICH-DORODNITSYN.
PURDUE UNIV LAFAYETTE IND
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The solution of the incompressible, laminar boundary-layer equations using the N-parameter integral method of Galerkin, Kantorovich and Dorodnitsyn is investigated. This method seeks to obtain an approximate solution of a partial differential equation with given boundary conditions by assuming the solution in functional form so that the boundary conditions for one variable are exactly satisfied. The approximating function is then specialized in such a manner as to obtain approximate satisfaction of the given equation. Solutions are presented for the similar flows and four types of nonsimilar flows flows with an abrupt change from an initial region of flow to a constant velocity flow, analytically prescribed external flows, experimentally determined external flows, and flows which proceed from a stagnation point to a separation point. These results indicate that the GKD method yields solutions which are uniformly better than classical approximation techniques and are of about the same accuracy as the usual exact numerical solution methods such as the series method, the Hartree-Womersley method and finite difference methods. Furthermore, solutions can be obtained as close to the separation point as computationally feasible. Author
- Numerical Mathematics
- Fluid Mechanics