Nonlinear Magnetohydrodynamic (MHD) Simulations using High-Order Finite Elements

C. R. Sovinec and C. C. Kim, University of Wisconsin-Madison;
D. D. Schnack and A. Y. Pankin, Science Applications International Corporation;
S. E. Kruger, Tech-X Corporation;
E. D. Held, Utah State University;
D. P. Brennan, Massachusetts Institute of Technology;
D. C. Barnes, University of Colorado-Boulder;
X. S. Li, Lawrence Berkeley National Laboratory;
D. K. Kaushik, Argonne National Laboratory;
S. C. Jardin, Princeton Plasma Physics Laboratory; and the NIMROD Team

Peak performance for magnetically confined fusion plasmas occurs near thresholds of instability for MHD-like modes that distort and possibly disrupt equilibrium conditions. Saturation effects often allow continued operation beyond the instability threshold, and in some cases the resulting pressure profile is better than what results by avoiding the instabilities.

Understanding this behavior is essential for achieving ignition in the proposed ITER experiment, and advances in large-scale numerical simulation have a central role. The evolution is nonlinear and sensitive to geometry, and physical effects at vastly different temporal and spatial scales act together to release free energy. Through support of the Center for Extended Magnetohydrodynamics and collaborating math and computer science centers, SCIDAC has advanced state-of-the-art modeling of macroscopic activity. Full adaptation of high-order finite elements in the NIMROD code permits accurate representation of extreme anisotropies imposed by the magnetic field. Of equal importance, collaboration with the Terascale Optimal PDE Simulation center has led to implementation of parallel direct methods for solving the sparse algebraic systems. The resulting performance improvements are presently being applied to investigate the evolution of Edge Localized Modes (ELMs). Continued interaction with our SCIDAC partners will be essential for modeling this activity with important drift effects in the nonlinear regime.