Numerical integration of the equations of the three-dimensional laminar boundary layer on lines of divergence

Abstract

Finite-difference methods are used for the numerical integration of the equations of the three-dimensional laminar boundary layer. The problem is then solved either in generalized similarity variables [1–4], or in Crocco variables [5]. In the particular case of a conical external flow the equations of the boundary layer are solved in [6, 7] by the method of integral ratios proposed by A.A. Dorodnitsyn [8] for solving the non-linear problems of aerohydrodynamics. In the particular case of a conical external flow the use of the method of integral ratios enables the problem to be reduced to the numerical integration of a system of ordinary differential equations, and in the general case, to the integration of first-order hyperbolic partial differential equations. As a result of this, the solution of problems by the method of integral ratios requires considerably less computer time to ensure an acceptable accuracy of the calculation, than finite-difference methods. This is an important advantage in performing systematic calculations. In this paper the method of integral ratios is used to solve the equations of the three-dimensional laminar boundary layer in generalized similarity variables, whereas in [6, 7] the problem is solved in Crocco variables. In particular examples the accuracy of the calculation is investigated as a function of the number of partition bands and of the distribution law of the boundaries of the bands, for the case where the exponential function is chosen for the orthogonalizing and approximating functions.