Nonlinear extended magnetohydrodynamics simulation using high-order finite elements

Peak performance for magnetically confined fusion plasmas occurs near thresholds of instability for macroscopic modes that distort and possibly disrupt equilibrium conditions. In some cases, however, the best approach is to exceed stability thresholds and rely upon nonlinear saturation effects. Understanding this behaviour is essential for achieving ignition in future burning plasma experiments, and advances in large-scale numerical simulation have an important role. High-order finite elements permit accurate representation of extreme anisotropies associated with the magnetic field, and a new implicit algorithm has been developed for advancing the two-fluid model. Implementation of parallel direct methods for solving the sparse matrices makes the approach practical. The resulting performance improvements are presently being applied to investigate the evolution of 'edge localized modes' including important drift effects.

[1]  F. Wagner,et al.  Regime of Improved Confinement and High Beta in Neutral-Beam-Heated Divertor Discharges of the ASDEX Tokamak , 1982 .

[2]  P. Snyder,et al.  Progress in the peeling-ballooning model of edge localized modes: Numerical studies of nonlinear dynamicsa) , 2005 .

[3]  L. Lao,et al.  Edge localized modes and the pedestal: A model based on coupled peeling–ballooning modes , 2002 .

[4]  Steven J. Plimpton,et al.  Nonlinear magnetohydrodynamics simulation using high-order finite elements , 2004 .

[5]  James F. Drake,et al.  Diamagnetic stabilization of ideal ballooning modes in the edge pedestal , 1999 .

[6]  Carl R. Sovinec,et al.  Hybrid kinetic-MHD simulations in general geometry , 2004, Comput. Phys. Commun..

[7]  Max D. Gunzburger,et al.  Mathematical Aspects of Finite Element Methods for Incompressible Viscous Flows , 1986 .

[8]  S. I. Braginskii.  Transport Processes in a Plasma , 1965 .

[9]  S. Kruger,et al.  NIMROD: A computational laboratory for studying nonlinear fusion magnetohydrodynamics , 2003 .

[10]  Douglas S. Harned,et al.  Accurate semi-implicit treatment of the hall effect in magnetohydrodynamic computations , 1989 .

[11]  W. Park,et al.  Plasma simulation studies using multilevel physics models , 1999 .

[12]  K Lerbinger,et al.  A new semi-implicit method for MHD computations , 1991 .

[13]  S. Kruger,et al.  Nonlocal closures for plasma fluid simulations , 2004 .

[14]  D. A. Knoll,et al.  A 2D high-ß Hall MHD implicit nonlinear solver , 2003 .

[15]  James Demmel,et al.  SuperLU_DIST: A scalable distributed-memory sparse direct solver for unsymmetric linear systems , 2003, TOMS.

[16]  Dalton D. Schnack,et al.  Semi-implicit magnetohydrodynamic calculations , 1987 .

[17]  J. Linker,et al.  Stability of Algorithms for Waves with Large Flows , 1999 .

[18]  Stephen C. Jardin,et al.  Implicit solution of the four-field extended-magnetohydrodynamic equations using high-order high-continuity finite elementsa) , 2004 .

[19]  R. L. Miller,et al.  Magnetohydrodynamic stability of tokamak edge plasmas , 1998 .