An Inverse Laminar Boundary Layer Problem with Assigned Wall Shear: The Mechul Function Revisited.
PENNSYLVANIA STATE UNIV UNIVERSITY PARK APPLIED RESEARCH LAB
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An inverse method is presented for accurately determining the pressure gradient distribution for specified wall shear in a two-dimensional laminar boundary layer. In the inverse formulation, the pressure gradient is treated as a dependent variable that is only a function of the streamwise coordinate. The method presented here is a reformulation of the mechul function scheme of Cebeci and Keller with additional techniques to increase the stability of the solution. These techniques include the use of fourth order splines to approximate normal derivatives and three point backward finite differences for the streamwise derivatives. Partial pivoting is also used in the solution of the block tridiagonal system resulting from the linearized equations of motion. The solution is obtained using the Newton iteration method. Numerical examples are presented for self-similar and non-similar solutions. Author
- Numerical Mathematics
- Fluid Mechanics