A GLOBALLY CONVERGENT MATRIX-FREE ALGORITHM FOR IMPLICIT TIME-MARCHING SCHEMES ARISING IN FINITE-ELEMENT ANALYSIS IN FLUIDS

A solution procedure for solving nonlinear time-marching problems is presented. The non-symmetric systems of equations arising from a Newton-type linearization of these time-marching problems are solved using an iterative strategy based on the generalized minimal residual (GMRES) algorithm. Matrix-free techniques leading to reduction in storage are presented. Incorporation of a linesearch algorithm in the Newton-GMRES scheme is discussed. An automatic time-increment control strategy is developed to increase the stability of the time-marching process. High-speed flow computations demonstrate the effectiveness of these algorithms.