Numerical solution of the Falkner–Skan equation using piecewise linear functions.(English)Zbl 1098.65110

Summary: We present a finite-element method for the solution of the Falkner–Skan equation. The method uses a coordinate transformation to map the semi-infinite domain of the problem to the unit interval $$[0,1]$$. By means of a suitable change of variables, the transformed third-order boundary value problem is further rewritten as a system of differential equations consisting of a second-order equation and a first-order equation. The second-order equation is approximated using a Galerkin formulation with piecewise linear elements, and the first-order equation is approximated using a centered-difference approximation. In the process of the initial transformation, a finite computational boundary is introduced. This boundary is obtained as part of the computational solution by imposing an additional asymptotic boundary condition. The solutions obtained thus are in excellent agreement with those obtained by previous authors.

MSC:

 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 76D10 Boundary-layer theory, separation and reattachment, higher-order effects 76M10 Finite element methods applied to problems in fluid mechanics
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References:

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