Choice of initial guess in iterative solution of series of systems arising in fluid flow simulations

Contemporary time stepping schemes applied to the solution of unsteady nonlinear fluid flow problems are considered. The iterative solution of arising series of linear and nonlinear systems and the choice of the initial guess are addressed. The computation of a better initial guess for two iterative linear system solvers (GCR and GMRES) is based on the history of the evolution problem solving. For implicitly discretized nonlinear evolution problems, a reduced model technique is developed for computing a better initial guess for the inexact Newton method. The computational effect of the chosen initial guess is compared with that of the standard (physically motivated) initial guess.