Finite-element discretizations of a two-dimensional grade-two fluid model

Some topological aspects of the magnetic reconnection phenomenon are summarized and recent numerical results, derived within a two-fluid model, of two-dimensional collisionless magnetic reconnection in presence of a strong guide field are reported. Both the Alfvèn and the whistler frequency range are investigated by including electron parallel compressibility effects that are related respectively to thermal effects and to density fluctuations. The Hamiltonian character of the system is emphasized as it drives the small scale dynamics through the presence of topological invariants. These determine the formation and the shape of small scale current and vorticity layers inside the magnetic island. Secondary fluid instabilities, mainly of the Kelvin–Helmholtz type, can destabilize these layers when a hydrodynamic type regime is achieved. The inclusion of parallel electron compressibility has stabilizing effects. In view of the limitations of the two-fluid modelling, possible developments are briefly discussed such as the inclusion of Larmor-radius corrections, in lieu of a fully kinetic approach.

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Bose condensate in the two-dimensional case, the λ-point, and the Thiess-Landau two-fluid model

Theoretical and Mathematical Physics ◽

10.1007/s11232-009-0045-z ◽

2009 ◽

Vol 159 (1) ◽

pp. 561-562 ◽

Cited By ~ 4

Author(s):

V. P. Maslov

Keyword(s):

Fluid Model ◽

Bose Condensate ◽

Dimensional Case ◽

Two Dimensional ◽

Two Fluid Model ◽

Λ Point ◽

Two Fluid

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A Two-Fluid Model of Mixing in a Two-Dimensional Enclosure

Journal of Heat Transfer ◽

10.1115/1.2830034 ◽

1998 ◽

Vol 120 (1) ◽

pp. 115-126 ◽

Cited By ~ 1

Author(s):

O. J. Ilegbusi ◽

M. D. Mat

Keyword(s):

Potential Energy ◽

Buoyancy Force ◽

Volume Fraction ◽

Fluid Model ◽

Two Dimensional ◽

Material Interface ◽

Thermal Buoyancy ◽

Two Fluid Model ◽

Nonisothermal Conditions ◽

Two Fluid

Mixing of fluids in a cavity under isothermal and nonisothermal conditions is studied with a two-fluid model. This model involves the solution of separate transport equations for zone-averaged variables of each fluid with allowance for interface transport of momentum and energy. The effects of thermal and potential energy driven convection as well as Prandtl number are investigated. The material interface is represented by the contour of the volume fraction separating the fluids. The effect of the buoyancy force due to the initial potential energy of the fluids is found to predominate over thermal buoyancy for comparable Grashof numbers.

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Hamiltonian vortices and reconnection in a magnetized plasma

Journal of Plasma Physics ◽

10.1017/s0022377898006655 ◽

1998 ◽

Vol 59 (4) ◽

pp. 727-736 ◽

Cited By ~ 30

Author(s):

B. N. KUVSHINOV ◽

V. P. LAKHIN ◽

F. PEGORARO ◽

T. J. SCHEP

Keyword(s):

Magnetic Flux ◽

Euler Equation ◽

Fluid Model ◽

Magnetized Plasma ◽

Two Dimensional ◽

Magnetic Islands ◽

Electron Momentum ◽

Lagrangian Form ◽

Two Fluid Model ◽

Two Fluid

Hamiltonian vortices and reconnection in magnetized plasmas are investigated analytically and numerically using a two-fluid model. The equations are written in the Lagrangian form of three fields that are advected with different velocities. This system can be considered as a generalization and extension of the two-dimensional Euler equation for an ordinary fluid. It is pointed out that these equations allow solutions in the form of singular current-vortex filaments, drift-Alfvén vortices and magnetic islands, and admit collisionless magnetic reconnection where magnetic flux is converted into electron momentum and ion vorticity.

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