(An) efficient noniterative finite differencemethod for the unsteady laminar boundary layers

Abstract

Many problems in the physics of fluid flow fall in the important category of unsteady viscous flow. In order to determine the friction drag and the rate of heat transfer through the surface of a body in dynamic motion, the unsteady viscous fluid flow must be investigated. A variety of methods, such as integral, series expansion and numerical methods, have appeared in the literature for the study of general unsteady boundary layers. In numerically simulating the unsteady boundary layers, iterative methods have been widely used because of the nonlinear terms in the governing equations. In this paper, an efficient noniterative implicit finite difference method is devised to solve the unsteady boundary layer problems. In order to eliminate the iterative procedure which became necessary due to the nonlinear convective terms, linearization of the finite difference equations, first developed by Beam and Warming for the compressible Navier-Stokes equations, is made for both the momentum boundary layer and the thermal boundary layer equations. The method is second-order accurate both in time and space. The method allows an exact spatial initial condition when a special similarity type transformation is introduced, by which the governing partial differential equations are reduced from bi-parabolic to mono-parabolic type at the spatial initial point. Application of the method is made to a variety of incompressible and compressible unsteady laminar boundary layers, with or without separation. We have demonstrated usefulness of the method for such diversified flows as the mixed flow on an inclined flat pate, the flow induced by a circular cylinder impulsively started from rest, the flow on an oscillatory circular cylinder, the unsteady compressible unsteady flow due to temperature field, and the compressible boundary layer flow excited by travelling expansion or compression waves. Comparison with the existing data has manifested excellency of the present method both in ac...