HIGH-ORDER SCHEME IMPLEMENTATION USING NEWTON-KRYLOV SOLUTION METHODS

Implementation of high-order discretization for the convective transpo rt terms in the inexact Newton method for a benchmark fluid flow and h eat transfer problem using various solution configurations at two Reyn olds numbers has been investigated. These configurations include fully consistent discretization of the Jacobian, preconditioner and residua l of the Newton method, low-order preconditioning using a matrix-free method to approximate the action of the Jacobian, and defect correctio n or low-order Jacobian and preconditioning. The residual in each case employs high order discretization to preserve the high-order solution . Two preconditioners, point incomplete lower-upper factorization ILU( k) and block incomplete lower-upper factorization BILU(k) for k = 0, 1 , 2 were applied. Also, ''one-way'' multigriding and capping the inner iterations was applied to determine the behavior of the solution perf ormance. It was determined that overall, the configuration using low-o rder preconditioning with ILU(1) BILU(1) or BILU(2) mesh sequencing, a nd inner linear solve iterations capped at the same value of the dimen sion n, used with the GMRES(n) iterative solver (i.e., no restarts), p erformed best for time, memory, and robustness considerations.