ENHANCED NONLINEAR ITERATIVE TECHNIQUES APPLIED TO A NONEQUILIBRIUM PLASMA-FLOW

We study the application of enhanced nonlinear iterative methods to th e steady-state solution of a system of two-dimensional convection-diff usion-reaction partial differential equations that describe the partia lly ionized plasma ow in the boundary layer of a tokamak fusion reacto r. This system of equations is characterized by multiple time and spat ial scales and contains highly anisotropic transport coefficients due to a strong imposed magnetic field. We use Newton's method to lineariz e the nonlinear system of equations resulting from an implicit, finite volume discretization of the governing partial differential equations , on a staggered Cartesian mesh. The resulting linear systems are neit her symmetric nor positive definite, and are poorly conditioned. Preco nditioned Krylov iterative techniques are employed to solve these line ar systems. We investigate both a modified and a matrix-free Newton-Kr ylov implementation, with the goal of reducing CPU cost associated wit h the numerical formation of the Jacobian. A combination of a damped i teration, mesh sequencing, and a pseudotransient continuation techniqu e is used to enhance global nonlinear convergence and CPU efficiency. GMRES is employed as the Krylov method with incomplete lower-upper (IL U) factorization preconditioning. The goal is to construct a combinati on of nonlinear and linear iterative techniques for this complex physi cal problem that optimizes trade-offs between robustness, CPU time, me mory requirements, and code complexity. It is shown that a mesh sequen cing implementation provides significant CPU savings for fine grid cal culations. Performance comparisons of modified Newton-Krylov and matri x-free Newton-Krylov algorithms will be presented.