Solutions of three-dimensional boundary layer equations by global methods of generalized differential-integral quadrature

Abstract

The global methods of generalized differential quadrature (GDQ) and generalized integral quadrature (GIQ) are applied to solve three-dimensional, incompressible, laminar boundary layer equations. The streamwise and crosswise velocity components are taken as the dependent variables. The normal velocity is obtained by integrating the continuity equation along the normal direction where the integral is approximated by GIQ approach with high order of accuracy. All the spatial derivatives are discretized by a GDQ scheme. After spatial discretization, the resultant ordinary differential equations are solved by the 4-stage Runge-Katta scheme. Application of GDQ-GIQ approach to a test problem demonstrated that accurate numerical results can be obtained using just a few grid points.