NEWTON-KRYLOV METHODS APPLIED TO A SYSTEM OF CONVECTION-DIFFUSION-REACTION EQUATIONS

We study the application of Newton-Krylov methods for the steady-state solution of the tokamak edge plasma fluid equations. This highly nonl inear system of two-dimensional convection-difusion-reaction partial d ifferential equations describes the boundary layer of a tokamak fusion reactor, These equations are characterized by multiple time and spati al scales. We use Newton's method to linearize the nonlinear system of equations resulting from the implicit, finite volume discretization o f the governing partial differential equations. The resulting linear s ystems are neither symmetric nor positive definite, and are poorly con ditioned. A variety of preconditioned Krylov iterative techniques are employed to solve these linear systems, and we investigate both standa rd and matrix-free implementations. A number of pseudo-transient conti nuation methods are investigated to increase the radius of convergence . While this system of equations describes a specific application, the general algorithm should benefit other applications requiring the sol ution of general reacting flow type equations.