A high-order implicit finite element method for integrating the two-fluid magnetohydrodynamic equations in two dimensions

Jardin, S.C.; Breslau, J.; Ferraro, N.M.

doi:10.1016/j.jcp.2007.07.003

Cited by 62 publications

(54 citation statements)

References 17 publications

(33 reference statements)

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“…Production runs were carried out with a grid of 400x200 points using mesh refinement in the Xpoint proximity with homomorphic grid functions: for the cases reported here, we used minimum step sizes and (for large (1) and (2) to keep gradients to the scale of the grid [11]. We demonstrated (and describe below) that the resulting reconnection rates and the macroscopic flows and fields were independent of the numerical coefficients used for these hyper-resistivity and -viscosity terms.…”

Section: Methodsmentioning

confidence: 99%

Reconnection in semicollisional, low-β plasmas

Schmidt¹,

Günter²,

Lackner³

2009

Physics of Plasmas

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Reconnection of semi-collisional, low-β plasmas is studied numerically for two model problems using a two-field description of the plasma including electron pressure effects (and hence kinetic Alfvén-wave dynamics). The tearing unstable Harris-sheet, with the global parameters of the GEMchallenge case shows a linear growth of the peak reconnection rate with the drift parameter s ρ when this scale is significantly larger than the resistive skin depth, and the island is smaller than the Harris sheet current layer width. As exemplary for a driven, rather than a spontaneous reconnection situation we study as second model system two coalescing islands, starting from a non-equilibrium situation.The peak reconnection rate again increases initially linearly with s ρ but saturates and becomes s ρ independent for larger values. In this saturated regime, no flux pile-up occurs, and the reconnection is limited by the rate of approach of the two coalescing islands. The qualitative differences between spontaneous and driven reconnection cases, and their scaling behaviour are best understood by considering the reconnection rate as a triple product of outflow Mach number, outflow to inflow channel width ratio, and magnetic energy density at a height s ρ above the X point.

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Section: Methodsmentioning

confidence: 99%

Reconnection in semicollisional, low-β plasmas

Schmidt¹,

Günter²,

Lackner³

2009

Physics of Plasmas

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“…(14) is canceled by the term proportional to n from the right-hand-side of Eq. (13). This general form of the linearized resistive-Hall-MHD equations shows clearly its marginally stable ideal-MHD solution, applicable to the "outer" region away from x ¼ 0:…”

Section: General Model Equationsmentioning

confidence: 61%

“…These range from earlier kinetic [2][3][4][5] and two-fluid [6][7][8][9] analyses, to recent works that use the gyrokinetic formalism. 10,11 Also recently, the development of large scale two-fluid simulation codes 12,13 has renewed the interest in accurate twofluid analytic results that could be used for code verification. Motivated by this, Refs.…”

Section: Introductionmentioning

confidence: 99%

Supersonic regime of the Hall-magnetohydrodynamics resistive tearing instability

Ahedo

Ramos

2012

Physics of Plasmas

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An earlier analysis of the Hall-magnetohydrodynamics (MHD) tearing instability [E. Ahedo and J. J. Ramos, Plasma Phys. Controlled Fusion 51, 055018 (2009)] is extended to cover the regime where the growth rate becomes comparable or exceeds the sound frequency. Like in the previous subsonic work, a resistive, two-fluid Hall-MHD model with massless electrons and zero-Larmor-radius ions is adopted and a linear stability analysis about a force-free equilibrium in slab geometry is carried out. A salient feature of this supersonic regime is that the mode eigenfunctions become intrinsically complex, but the growth rate remains purely real. Even more interestingly, the dispersion relation remains of the same form as in the subsonic regime for any value of the instability Mach number, provided only that the ion skin depth is sufficiently small for the mode ion inertial layer width to be smaller than the macroscopic lengths, a generous bound that scales like a positive power of the Lundquist number. V C 2012 American Institute of Physics. [http://dx

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“…To evaluate our new ILU strategies, we have chosen 54 matrices from the following sources: Matrix Market [17], University of Florida Sparse Matrix collection [5], and five matrices from the fusion device simulation [14]. We use COLAMD for column permutaion and MC64 for equilibration and row permutation.…”

Section: Notations and Experimental Setupmentioning

confidence: 99%

A Supernodal Approach to Incomplete LU Factorization with Partial Pivoting

Shao

2011

ACM Trans. Math. Softw.

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We present a new supernode-based incomplete LU factorization method to construct a preconditioner for solving sparse linear systems with iterative methods. The new algorithm is primarily based on the ILUTP approach by Saad, and we incorporate a number of techniques to improve the robustness and performance of the traditional ILUTP method. These include the new dropping strategies that accommodate the use of supernodal structures in the factored matrix. We present numerical experiments to demonstrate that our new method is competitive with the other ILU approaches and is well suited for today's high performance architectures.

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A high-order implicit finite element method for integrating the two-fluid magnetohydrodynamic equations in two dimensions

Cited by 62 publications

References 17 publications

Reconnection in semicollisional, low-β plasmas

Reconnection in semicollisional, low-β plasmas

Supersonic regime of the Hall-magnetohydrodynamics resistive tearing instability

A Supernodal Approach to Incomplete LU Factorization with Partial Pivoting

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