Fully Implicit, Jacobian-Free, Newton-Krylov Methods in Production Level MHD Fusion Codes

The DOE's Office of Fusion Energy Sciences (OFES) has spent tens of millions of dollars developing simulation tools that assist in understanding the requirements for stable and sustained fusion. However, the main magnetohydrodynamic (MHD) OFES simulation tools use methods that have numerical stability limitations dictated by the plasma velocity. Thus, there exists an urgent need to introduce modern computational algorithms into these OFES simulation tools to maximize their efficiency on petascale computing architectures. Solving the nonlinear system of equations presents a challenge, but recent work that has demonstrated the existence of a preconditioner that has the potential to scale remarkably on petascale machines. This project will develop an implicit, nonlinear solver for two-dimensional (2D) problems. The initial focus will be on the momentum equations within the MHD system; then, the work will be extended to the full set of equations for 2D problems. Commercial Applications and other Benefits as described by the awardeeThe expertise gained in this project should lead to consulting work from the NIMROD project and also from the Center of Extended Magnetohydryodynamic Modelling. Other opportunities also should exist beyond the DOE.