Convergence Acceleration of Relaxation Solutions for Transonic Flow Computations Mohamed

The problem of how to speed up the convergence of currently available iterative methods for transonic flow computations with minimal alterations in computer programing and storage is considered. A cyclic iterative procedure applying nonlinear sequence transformations akin to those of Aitken and Shanks is developed. Based on the power method, the errors in these sequence transformations are studied. Examples testing the procedure for model Dirichlet problems and for transonic thin airfoil problems show that savings in computer time of a factor of two to five, or more, is generally possible, depending on accuracy requirements and the particular iterative procedure used. I. Introduction M ANY current methods of fluid dynamic computations make use of relaxation procedures. There are several aspects of the computation that considerably limit the usefulness and potentiality of these programs. One is the slow convergence with respect to iterations of the flowfield calculation, and, hence, costly computer time. This paper presents studies on how to speed up the convergence of currently available iterative procedures with minimal alterations in computer programing and storage requirements. To see the need of the convergence acceleration, we may take as an example the finite-difference solution to Dirichlet's problem on a unit square. The convergence rate of practical iterative procedures (Jacob!, Gauss-Seidel, Successive Over