A Finite-Volume Algorithm for Three-Dimensional Magnetohydrodynamics on an Unstructured, Adaptive Grid in Axially Symmetric Geometry

Schnack, D. D.; Lottati, I.; Mikić, Z.; Satyanarayana, P.

doi:10.1006/jcph.1998.5873

Cited by 21 publications

(16 citation statements)

References 28 publications

(56 reference statements)

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“…Finite elements and flux-aligned grids have recently been shown to be valuable for resolving the anisotropic operators ͑various forms of B · ٌ͒ of nonideal MHD. 28 Specialized implicit methods have been developed to deal with temporal stiffness, [21][22][23][24][25][26][27][28][40][41][42][43][44] and have enabled accurate computations to proceed with CFL numbers in excess of 10. 4,5 While all of these approaches require solution of large algebraic systems at every time step, the Hermitian character of the relevant operators can be used to facilitate computation.…”

Section: A General Considerationsmentioning

confidence: 99%

“…22,24 A benefit that arises with finite elements is that the anisotropic operator that distinguishes the fast, shear, and slow modes of the MHD spectrum 43 is straightforward to implement and, by construction, results in a Hermitian matrix for the velocity advance. 28 For the subdominant plasma flow in resistive MHD, predictor-corrector steps for advective terms can be retained.…”

Section: Temporal Discretizationmentioning

confidence: 99%

“…[14][15][16][17][18][19][20][21][22][23][24][25][26][27][28] These usually employ strongly implicit time advance algorithms, and are able to advance the solution accurately and stably over very large time steps. The advantage is that all the underlying physics is retained, the model remains valid across a wide range of parameters, the boundary conditions are obvious, and the same algorithm can be applied to a wide variety of problems pertaining to magnetized plasmas.…”

Section: Introductionmentioning

confidence: 99%

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Computational modeling of fully ionized magnetized plasmas using the fluid approximation

et al. 2006

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Strongly magnetized plasmas are rich in spatial and temporal scales, making a computational approach useful for studying these systems. The most accurate model of a magnetized plasma is based on a kinetic equation that describes the evolution of the distribution function for each species in six-dimensional phase space. High dimensionality renders this approach impractical for computations for long time scales. Fluid models are an approximation to the kinetic model. The reduced dimensionality allows a wider range of spatial and/or temporal scales to be explored. Computational modeling requires understanding the ordering and closure approximations, the fundamental waves supported by the equations, and the numerical properties of the discretization scheme. Several ordering and closure schemes are reviewed and discussed, as are their normal modes, and algorithms that can be applied to obtain a numerical solution.

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Section: A General Considerationsmentioning

confidence: 99%

Section: Temporal Discretizationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Computational modeling of fully ionized magnetized plasmas using the fluid approximation

et al. 2006

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“…For these reasons we are led to try adaptive unstructured mesh methods. Unstructured meshes have also been used in other computational MHD approaches [6]. We have chosen to apply these methods to two-dimensional, incompressible MHD, using a stream function approach to enforce the divergence-free conditions on the magnetic and velocity fields.…”

Section: Mhdmentioning

confidence: 99%

An Adaptive Finite Element Method for Magnetohydrodynamics

Strauss¹,

Longcope²

1998

Journal of Computational Physics

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A finite element discretization for two-dimensional MHD is described. The elements are triangles with piecewise linear basis functions. The main computational difficulty is the accurate calculation of the current. The most effective solution is to employ a current-vorticity advection formulation of the equations. Acceptable results can also be obtained with a two-step calculation of the current from the vector potential. Mesh operations are described to reconnect and refine the mesh adaptively in the vicinity of nearly singular currents to improve magnetic flux conservation. Example computations of the coalescence instability, tilt mode, and divertor tokamak equilibrium, validating and illustrating the method, are presented. The simulations show the formation of current sheets, with the current density increasing exponentially in time. During this increase, the grid of initially ∼10 4 points adapts to provide resolution comparable to a uniform grid of up to 1.6 × 10 8 grid points.

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“…We employ a two-dimensional axisymmetric resistive compressible Hall MHD code -modified TRIangular Magneto-hydrodynamics (TRIM) [25], to simulate the time-evolution of electro-magnetic fields, momentum density and plasma density in MRX. In doing so, we solve the following set of resistive Hall MHD equations in cylindrical geometry with no-slip perfectly conducting boundaries:…”

Section: Hall Mhd Model and Mrxmentioning

confidence: 99%

Hall MHD Modeling of Two-dimensional Reconnection: Application to MRX Experiment

Lukin¹,

Jardin²

2003

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A two-dimensional resistive Hall magneto-hydrodynamics (MHD) code is used to investigate the dynamical evolution of driven reconnection in the Magnetic Reconnection Experiment (MRX). The initial conditions and dimensionless parameters of the simulation are set to be similar to the experimental values. We successfully reproduce many features of the timeevolution of magnetic configurations for both co-and counter-helicity reconnection in MRX. The Hall effect is shown to be important during the early dynamic X-phase of MRX reconnection, while effectively negligible during the late "steady-state" Y-phase, when plasma heating takes place. Based on simple symmetry considerations, an experiment to directly measure the Hall effect in MRX configuration is proposed and numerical evidence for the expected outcome is given.

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A Finite-Volume Algorithm for Three-Dimensional Magnetohydrodynamics on an Unstructured, Adaptive Grid in Axially Symmetric Geometry

Cited by 21 publications

References 28 publications

Computational modeling of fully ionized magnetized plasmas using the fluid approximation

Computational modeling of fully ionized magnetized plasmas using the fluid approximation

An Adaptive Finite Element Method for Magnetohydrodynamics

Hall MHD Modeling of Two-dimensional Reconnection: Application to MRX Experiment

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