On the method of numerical integration of 2D boundary layer equations

A. Bartulis - E. Shcherbinin

Institute of Physics, University of Latvia, Salaspils-1, LV-2169, Latvia

Abstract
The generic problem in the theory of boundary layer is two-point boundary value problem, when some of the boundary conditions are given at the one boundary but remainder at the other, as a rule at infinity. At the numerical integration of the ordinary differential equations it is desirable to have initial value problem, when all boundary conditions are given at one boundary. Unfortunately, there are practically not described the methods of receiving of solutions for such situations in monographic literature, besides T. Y. Na work, in which shooting method was described. The essence of the shooting method is modifying of missing boundary value to satisfy the required boundary conditions with necessary accuracy. This procedure is rather difficult even only one boundary condition is missing, as it takes place in 2D boundary layer problems. More complex problem became in case of two missing boundary conditions, when we need shoot in 2D space, that occur in problems with thermal convection. In present work the united approach of numerical solution of boundary layer problems have been offered. These approach completely takes off the two-point boundary value problem in pure hydrodynamic flows and problem with two missing boundary conditions leads to one missing boundary condition problem in flow with natural thermal convection. Considerations of approach have been made in following sequence: hydrodynamic, natural convection and mixed flows. Peculiarity of this approach are shown by using both boundary and integral conditions, and also for solving these problems at the presence of magnetic field and if medium is electrically conducting. Table 2, Figs 12, Refs 9.