Locally analytic numerical method and application to viscous internal and external flows

Abstract

A locally analytic numerical method is developed to predict the two-dimensional internal and external steady laminar flow of an incompressible viscous fluid. In this method, analytic solutions of locally linearized partial differential equations are incorporated into the numerical solution. This is accomplished by dividing the flow field into computational grid elements. In each individual element, the nonlinear convective terms of the Navier-Stokes equations are locally linearized, with analytic solutions then determined. The solution for the complete flow field is obtained by the assembly of these locally analytic solutions. The nonlinear character of the complete flow field is preserved as the flow is only locally linearized, i.e. independently linearized solutions are obtained in individual grid elements. This locally analytic numerical solution method is used to analyze the viscous flow in several internal and external flow configurations, with the prediction of flow development, reversal, separation, and reattachment demonstrated over a range of moderate values of the Reynolds number. In particular, three internal and one external flow configurations are investigated, with predictions obtained for entrance flow development in a straight channel, the flow through a sudden expansion, i.e. over a backward step, the flow in a diffuser, and the flow past a flat plate airfoil over a range of mean flow incidence angle values.