The Falkner-Skan equation: Numerical solutions within group invariance theory
A model describing the flow of a fluid past a wedge is considered. The governing differential equation is the classical Falkner-Skan equation with relevant boundary conditions. In this problem, a boundary condition at infinity is imposed which is not suitable for numerical treatment. In order to overcome this difficulty, a free boundary formulation of the problem is introduced. The author devises an iterative transformation method that reduces the free boundary formulation to a sequence of initial value problems. Moreover, as far as the value of the wall shear stress is concerned, the author proposes a numerical test on convergence. The usefulness of this approach is illustrated by considering the wall shear stress for the classical Homann and Hiemenz flows. Numerical results obtained are compared with those reported in literature.
scientific article; zbMATH DE number 817319
scientific article