Abstract
The present work is devoted to accelerate the nonlinear convergence of Newton-Krylov methods for solving fully implicit formulation in multiphase flow. The basic approach is to perform secant (Broyden) updates restricted to the Krylov subspace generated by the GMRES iterative solver. This approach is introduced as Krylov-secant methods. One of the most attractive features of these methods is to perform a sequence of rank-one updates without explicitly recalling the computation or action of the Jacobian matrix. Implications of these updates in line-search globalization strategies, computation of dynamic tolerances (forcing terms) and in the use of preconditioning strategies are presented. Numerical results show significant improvements over traditional implementations especially in those cases where nonlinearities increase due to stringent pressure and saturation changes.
