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

We propose in this paper a technique to accelerate the convergence of the Newton method to solve non-linear unsteady CFD problems. The principle relies on an effective way to obtain a better solution for the current time step than the solution of the previous time step. This is performed on a reduced model computed with a Proper Orthogonal Decomposition of some solution computed at some previous time step. The developed methodology fits the grid computing design with a client server approach to compute the POD components necessary for the acceleration. We will shows on several flows configurations the effective computational saving obtained with the proposed technique. Let us recall briefly the fully implicit discretizations of unsteady nonlinear problems. Let L(u) be a nonlinear discrete operator representing a spatial approximation of a parabolic boundary value problem. The simplest robust technique for time approximation of unsteady problems is the backward Euler time stepping: