A finite element convergence study for accelerating flow problems

Abstract

Abstract The convergence properties of several non‐linear solution procedures were examined with respect to the accelerated flow of a fluid in a converging channel (the Hamel problem), using two different finite element computer programs with different elemental construction. The Reynolds number varied from that for creeping flow to 1088 without exceeding the radius of convergence. Special attention was given to the successive substitution and Newton–Raphson solution algorithms, with a significant advantage in rate of convergence noted for the latter.