Semi-implicit magnetohydrodynamic calculations
Journal of Computational Physics
A critical analysis of the modified equation technique of Warming and Hyett
Journal of Computational Physics
Derivation of implicit difference schemes by the method of differential approximation
Journal of Computational Physics
Stability of algorithms for waves with large flows
Journal of Computational Physics
On balanced approximations for time integration of multiple time scale systems
Journal of Computational Physics
SuperLU_DIST: A scalable distributed-memory sparse direct solver for unsymmetric linear systems
ACM Transactions on Mathematical Software (TOMS)
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
A 2D high-ß Hall MHD implicit nonlinear solver
Journal of Computational Physics
Jacobian-free Newton-Krylov methods: a survey of approaches and applications
Journal of Computational Physics
Nonlinear magnetohydrodynamics simulation using high-order finite elements
Journal of Computational Physics
A fully implicit numerical method for single-fluid resistive magnetohydrodynamics
Journal of Computational Physics
Journal of Computational Physics
An iterative semi-implicit scheme with robust damping
Journal of Computational Physics
The XTOR code for nonlinear 3D simulations of MHD instabilities in tokamak plasmas
Journal of Computational Physics
Bézier surfaces and finite elements for MHD simulations
Journal of Computational Physics
Calculations of two-fluid magnetohydrodynamic axisymmetric steady-states
Journal of Computational Physics
Accurate semi-implicit treatment of the Hall effect in magnetohydrodynamic computations
Journal of Computational Physics
Review of implicit methods for the magnetohydrodynamic description of magnetically confined plasmas
Journal of Computational Physics
Hi-index | 31.45 |
A temporally staggered algorithm for advancing solutions of the two-fluid plasma model is analyzed with von Neumann's method and with differential approximation. The implicit leapfrog algorithm [C.R. Sovinec et al., J. Phys. Conf. Series 16 (2005) 25-34] is found to be numerically stable at arbitrarily large time-step when the advective, Hall, and gyroviscous terms are temporally centered in their respective advances and the coefficient of the semi-implicit operator meets the criterion found for basic hyperbolic systems. Numerical instability with forward or backward differencing of advection is evident as an ill-posed equation in the differential approximation for a simplified system. At large time-step, the accuracy of the algorithm is comparable to that of the Crank-Nicolson method for all plane waves except the parallel mode that is sensitive to the ion cyclotron resonance. An implementation reproduces theoretical results on the transition from resistive magnetohydrodynamics to two-fluid reconnection in a sheared-slab linear tearing mode. A nonlinear three-dimensional computation in toroidal geometry shows an increasing exponentiation rate of kinetic energy as magnetic reconnection from an internal kink mode changes from current-sheet to 'X-point' geometry.