A Composite Finite Difference Scheme for Subsonic Transonic Flows (RESEARCH NOTE).


1 Mechanical Engineering, Sharif University of Technology

2 Mechanical Engineering, University of Guilan


This paper presents a simple and computationally-efficient algorithm for solving steady two-dimensional subsonic and transonic compressible flow over an airfoil. This work uses an interactive viscous-inviscid solution by incorporating the viscous effects in a thin shear-layer. Boundary-layer approximation reduces the Navier-Stokes equations to a parabolic set of coupled, non-linear partial differential equations. The resulting system of partial differential equations is then solved using an efficient implicit finite difference scheme. A non uniform mesh is used and the eddy viscosity concept models the turbulent Reynolds stress terms. The solution for the steady subsonic and transonic Euler equations is obtained using an upwind finite-volume scheme. The scheme is based on artificial viscosity in the governing equations to provide the necessary dissipation for numerical stability. The system of equations is linearized by a Newton method and the resulting fully coupled system of algebraic equations is solved. Convergence of the method is demonstrated to be robust, taking very few iterations to reach machine accuracy. Shock-Capturing methods extends the applicability of the scheme to situations with shocks. The two schemes are coupled and an iterative procedure is used to link the results of the inviscid and viscous flow fields. Computations are made for a series of flows. Results for NACA 0012 airfoil flows are presented and compared with experimental data and other computational results.