COMPUTATIONAL OPTIMIZATION FOR INTEGRAL TRANSFORM ALGORITHMS APPLIED TO THE LID-DRIVEN CAVITY FLOW PROBLEM

Abstract

An analysis is presented of the computational optimization for integral transform algorithms using the streamfunction only formulation of the Navier-Stokes equations, as applied to the steady incompressible laminar flow of a Newtonian fluid in two-dimensional formulation. The classical lid-driven rectangular cavity flow problem is considered in order to revise the conventional development of the Generalized Integral Transform Technique (GITT). The GITT is applied transforming the partial differential equation into a system of coupled ordinary differential equations, which is numerically solved by a general algorithm for boundary value problems, using a subroutine from the IMSL library with automatic error control. The conventional algorithm written in FORTRAN language is modified and tested seeking its optimization. A few different strategies of applying the technique are considered to achieve improved computational performance and allowing the inspection of convergence rates in the eigenfunction expansion of the original potentials for high Reynolds numbers. These different algorithm alternatives are analyzed and the relative merits are discussed. Results for different values of the Reynolds number and cavity aspect ratios are presented in tabular and graphical forms and fully converged results are critically compared against previously published findings.