A Parameter Robust Method for a Problem with Free Boundary Layers
by
Ali R. Ansari
Department of Mathematics, University of Limerick, Limerick, Ireland
Coauthors: Alan F. Hegarty (Department of Mathematics, University of Limerick), G.I.Shishkin (Institute of Mathematics and Mechanics, Russian Academy of Sciences)

We consider the problem of a two-dimensional laminar jet of incompressible fluid flowing into a stationary medium of the same fluid. The physical situation is that of an infinitely long narrow slit which forms the source of the jet. It is sometimes referred to as a free boundary layer problem. The equations of motion are the same as the boundary layer equations of Prandtl's problem, i.e., flow over an infinite flat plate, but with different boundary conditions. Numerical experiments show that, using an appropriate piecewise uniform mesh, numerical solutions are obtained which are parameter robust with respect to both the number of mesh nodes and the number of iterations required for convergence.

Date received: February 25, 2000