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Numerical solution of the Navier-Stokes equations for symmetric laminar incompressible flow past a parabola

Symmetric laminar incompressible flow past a parabolic cylinder is considered for all Reynolds numbers. In the limit as the Reynolds number based on nose radius of curvature goes to zero, the solution for flow past a semi-infinite flat plate is obtained. All solutions are found by using an implicit alternating direction method to solve the time-dependent Navier-Stokes equations. The solutions found are compared with various other exact and approximate solutions. Results are presented for skin friction, surface pressure, friction drag and pressure drag. The numerical method developed is of particular interest since it combines the alternating direction method with the implicit method for solving the boundary-layer equations. This leads to fast convergence and may be of use in other problems.