Comparison of iterative and direct solution methods for viscous flow problems

A quantitative comparison is conducted for several numerical solution techniques used in two-dimensional viscous flow problems, including separated flows, at moderate-to-high Re numbers. Using Newton's linearization and Gaussian elimination with the partial pivoting to solve the finite-difference equations of the coupled system for the stream function, phi, and vorticity, omega, simultaneously, yields a very robust algorithm which converges quadratically. The combination of a direct solver for the stream-function equation and line-relaxation method for the coupled stream-function and vorticity equations yields the fastest scheme. (O.C.)