A pseudospectral algorithm for three-dimensional magnetohydrodynamic simulation

TL;DR: NIMROD as discussed by the authors is a code development project designed to study long-wavelength, low-frequency, nonlinear phenomena in toroidal plasmas with realistic geometry and dynamics.

TL;DR: The authors study the hypothesis that sawtooth oscillations or internal disruptions are the result of a cyclic process in which the plasma core is resistively heated until the safety factor drops below unity, causing the m = 1 tearing mode to become unstable, to grow with an accelerating growth rate, and to flatten the electron temperature and safety factor profiles.

TL;DR: For a certain set of boundary and initial conditions, the compressible codes predict field reversal maintenance while the incompressible codes do not, and compressibility is an important feature of RFP physics.

TL;DR: In this article, an efficient algorithm for the solution of compressible magnetohydrodynamic equations in a three-dimensional geometry is presented, where compressional Alfven waves are treated implicitly, thus greatly increasing the stable time step of the calculation and making it possible to study magnet-hydrodynamic (MHD) phenomenon on resistive time scales.

TL;DR: Spectral Methods Survey of Approximation Theory Review of Convergence Theory Algebraic Stability Spectral Methods Using Fourier Series Applications of algebraic stability analysis Constant Coefficient Hyperbolic Equations Time Differencing Efficient Implementation of Spectral Method as discussed by the authors.

TL;DR: In this paper, the stability of a plane current layer is analyzed in the hydromagnetic approximation, allowing for finite isotropic resistivity, and the effect of a small layer curvature is simulated by a gravitational field.

TL;DR: In this article, Galerkin (spectral) methods are explored for the numerical simulation of incompressible flows within simple boundaries and pseudospectral approximations are introduced in order to handle more complicated dynamical interactions in more complicated geometries.

TL;DR: In this paper, an algorithm for the rapid calculation of the convolution sums appearing in the Fourier-transformed Navier-Stokes equations in three dimensions is given. But the algorithm is only a factor of 4 more efficient than previously suggested algorithms.