Robust and accurate numerical methods applied to the edge plasma equations

We present results from advanced numerical methods development in support of dissipative divertor research. Results are presented from simulations using a combined edge plasma / Navier-Stokes neutral transport model. The tokamak edge plasma fluid equations are known to contain a wide disparity in time scales and space scales. They also contain extreme nonlinearities in transport coefficients and reaction rates. Obtaining steady-state solutions is often the motivation of the simulation rather than following a time accurate transient. The multiple time scales and the strong nonlinearities have motivated research into the use of Newton-Krylov algorithms, which form the basis of the UEDGE code. Improvements are presented which increase the radius of convergence of Newton's method, enhance the parallel nature of the algorithm, and increase the accuracy of the discretization. The performance of a pseudo-transient technique, which adoptively transitions to a steady-state solution is studied In a Newton-Krylov algorithm, formation and application of the preconditioning matrix is usually the bottleneck to parallelization. We present results employing domain decomposition preconditioning (additive Schwarz) to the edge plasma equations and discuss the parallel performance of this Newton-Krylov-Schwarz algorithm. Traditionally, edge plasma fluid codes have used first-order accurate methods for discretizing the convective derivatives. We study the effects of using a higher-order, monotone, discretization on both solution accuracy and algorithm performance. Additionally, we present the latest advancements in our combined edge plasma / Navier-Stokes neutral transport model