Robust, Scalable, Accurate, and Efficient Computational Formulation and Solution Methods for Plasma Transport/Reaction and Extended MHD Simulations

This multidisciplinary research project is to develop advanced numerical formulations and solution methods for plasma transport/ reaction (PTR) and extended magnetohydrodynamics (XMHD) systems. These systems are strongly coupled, highly nonlinear and characterized by multiple physical phenomena that span a very large range of length and time scales, and lead to systems of nonlinear PDEs that are extremely challenging to solve numerically. Our synergistic approach places strong focus on integration of physics- compatible spatial discretizations, fully-implicit time integration methods and robust and efficient nonlinear/linear iterative solution methods for PTR and XMHD. Among the key research areas will be the formulation and analysis of stable and accurate compatible spatial discretizations, the development and evaluation of advanced scalable Newton-Krylov iterative solution methods for large-scale nonlinear/ linear systems, and the design of robust and efficient physics-based preconditioners for these methods.