Premium
A unified approach to direct and inverse boundary layer solutions
Author(s) -
Kaufman K. C.,
Hoffman G. H.
Publication year - 1988
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.1650081102
Subject(s) - mathematics , discretization , mathematical analysis , boundary value problem , linearization , boundary layer , nonlinear system , mechanics , physics , quantum mechanics
A unified approach is presented for solving the two‐dimensional incompressible boundary layer equations. Solutions are obtained for direct and inverse options using the same equation formulation by a simple interchange of boundary conditions. A modified form of the mechul function scheme obtains inverse solutions with specification of transformed wall shear, skin friction coefficient or displacement thickness distributions. Direct solutions may be obtained without altering the block tridiagonal structure of the system by simply requiring no corrections on the streamwise pressure gradient parameter. Fourth‐order spline discretization approximates normal derivatives with two‐ and three‐point backward differences approximating streamwise derivatives, yielding a fully implicit solution method. The resulting spline/finite difference equations are solved by Newton‐Raphson iteration together with partial pivoting. The results of the study demonstrate the importance of proper linearization of all equations. The successful use of spline discretization is also tied to the use of strong two‐point boundary conditions at the wall for cases involving reversed flow. Numerical solutions are presented for several non‐similar flows and compared with published results.