Mixed velocity, stress, current, and potential boundary conditions for stationary MHD flow
✍ Scribed by M. Charina; A.J. Meir; P.G. Schmidt
- Publisher
- Elsevier Science
- Year
- 2004
- Tongue
- English
- Weight
- 625 KB
- Volume
- 48
- Category
- Article
- ISSN
- 0898-1221
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✦ Synopsis
This paper is concerned with a boundary-value problem, describing the stationary flow of a viscous, incompressible, electrically conducting fluid, confined to a bounded region of space, under mixed boundary conditions. The flow is governed by the Navier-Stokes equations, Ohm's law, and the Biot-Savart law; the boundary conditions involve the velocity field, stress tenser, electric current density, and electric potential. We derive a mixed variational formulation of the problem, which lends itself naturally to finite-element discretizations, and prove the existence and uniqueness of a (small) solution under the assumption of sufficiently small data. (~) 2004 Elsevier Ltd. All rights reserved.
geywords--Mixed variational methods, Finite elements, Magnetohydrodynamics, Navier-Stokes equations, Maxwell's equations.
Byron Burch (author of beer brewing books) writes: "When brewers speak of boundless energy that reflects a passionate love of beer and brewing, and of reason revealed as a depth of technical knowledge and understanding, all embodied in a single person, obviously we're thinking of George Fix." This statement is equally true when brewers, and beer and brewing, are replaced by mathematicians and mathematics, respectively. The second author remembers fondly the finiteelement class taught by George Fix (out of Strang and Fix, of course) which he attended as a young graduate student. George's enthusiasm for mathematics will be sorely missed.