AN IMPROVED GMRES METHOD FOR SOLVING VISCOELASTIC FLUID-FLOW PROBLEMS

We present a modified generalised minimal residual (GMRES) method for the solution of viscoelastic fluid flow problems. Belonging to a class of so-called Krylov-Newton methods, it allows the solution of non-linear systems without computation of a potentially large Jacobian matrix. For viscoelastic fluids, GMRES can be used to decouple the computation of the velocity and pressure from that of the stress tensor. This substantially reduces the storage requirement with respect to a full Newton method. Our method has shown to be much more efficient than the Picard algorithm. Numerical results are also presented.