POD acceleration of fully implicit solver for unsteady nonlinear flows and its application on grid architecture

A method for the acceleration of a fully implicit solution of nonlinear unsteady boundary value problem is presented. The principle of acceleration is for provide to the inexact Newton backtracking method a better initial guess, for the current time step, than the conventional choice from the previous time step. This initial guess is built on the reduced model obtained by a proper orthogonal decomposition of solutions at the previous time steps. This approach is appealing to GRID computing: spare processors may help to improve the numerical efficiency and to manage the computing in a reliable way.