Numerical Solution of Corner Flow Problem Using an Alternating Direction Implicit Method.

摘要

The axial corner flow problem has been analysed for the general compressible case. The equations describing this flow in terms of similarity variables are nonlinear elliptic partial differential equations. For the purpose of developing an efficient method for solving these compressible flow equations,and ADI (alternating direction implicit) method is formulated for the corresponding limiting case of incompressible corner flow. An optimization study of the method has been carried out in order to maximize the solution convergence rate while maintaining its stability and accuracy. The results obtained by the present method compare well with the available results due to the Gauss Seidel explicit method. The influence of symmetry boundary on the solution convergence rate has been studied and the appropriate manner of specifying this boundary condition for numerical computation has been established. The boundary condition on the vorticity function at the wall has been analyzed,and the advantages of the implicit treatment of this boundary condition over explicit treatment are presented. The effect of total second order accuracy of the ADI method in light of numerical stability and accuracy of the solution of the finite difference equations is indicated. The ADI method is seen to possess certain advantages over the Gauss Seidel explicit method. (Author)