Nonlinear Fusion MHD Simulation Using High-Order Finite Elements


The NIMROD code is being used for modeling nonlinear fusion MHD in a variety of configurations. Geometric flexibility and accuracy in extremely anisotropic conditions are achieved with high-order finite elements, while a semi-implicit temporal advance addresses the stiffness of multiple time-scales. The two approaches work particularly well together. The spatial representation preserves the symmetry of complicated self-adjoint differential operators, like the ideal linear force operator. Conversely, the finite element method is a variational approach to spatial representation when the implicit terms are self-adjoint, as is the case with our semi-implicit temporal advance. The implicit part of the velocity advance is based on Ref. [1] and resembles numerical systems for ideal MHD eigenvalue computations [2]; however, the temporally converged spectrum of the marching algorithm is determined by the explicit terms. Furthermore, the nonideal system of equations solved in nonlinear problems requires a solution space of higher continuity than those used for ideal MHD, where singular behavior is more severe. Convergence rates are computed in relevant test cases and are shown to compare well with the results of numerical analysis.

1. K. Lerbinger and J. F. Luciani, J. Comput. Phys. 97, 444 (1991).
2. R. Gruber and J. Rappaz, Finite element methods in linear ideal magnetohydrodynamics (Springer-Verlag, 1985).
Last modified: Fri Jun 18 18:45:08 EDT 2004