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We are concerned with the steady flow of a conducting fluid, confined to a bounded region of space and driven by a combination of body forces, externally generated magnetic fields, and currents entering and leaving the fluid through electrodes attached to the surface. The flow is governed by the Navier–Stokes equations (in the fluid region) and Maxwell's… (More)

- W. J. LAYTON, A. J. MEIR
- 1997

We describe and analyze a two-level finite-element method for discretizing the equations of stationary, viscous, incompressible magnetohydrodynamics (or MHD). These equations, which model the flow of electrically conducting fluids in the presence of electromagnetic fields, arise in plasma physics and liquid-metal technology as well as in geophysics and… (More)

We present a novel approach to the mathematical analysis and computational simulation of fully three-dimensional, nonlinear, viscous, incompressible MHD ow in complex conngurations involving several liquid and solid conductors. Such conngurations arise in numerous metallurgical processes. Employing the current density rather than the magnetic eld as the… (More)

- A. J. Meir, P. G. Schmidt
- 1998

Much research effort has recently been devoted to the electromagnetic control of saltwater flows, exploiting the macroscopic interaction of saltwater with electric currents and magnetic fields. This interaction is governed by the equations of viscous incompressible MHD, essentially, the Navier-Stokes equations coupled to Maxwell's equations. A major problem… (More)

We describe a novel approach to the mathematical modeling and computational simulation of fully three-dimensional, electromagnetically and thermally driven liquid-metal flow. The phenomenon is governed by the Navier-Stokes equations, Maxwell's equations, Ohm's law, and the heat equation, all nonlinearly coupled via Lorentz and electromotive forces, buoyancy… (More)

The heat equation posed on the half-line may be used as a simple mathematical model describing the operation of an amperometric ion sensor. These sensors represent the next generation of sensors that are in routine use today. Such sensors may be used to measure ion concentrations in the laboratory, for clinical analysis, environmental monitoring, process… (More)

A numerical solution for the prediction of the time-dependent potential response of a polymeric-based ion-selective electrode (ISE) is presented. The model addresses short- and middle-term potential drifts that are dependent on changes in concentration gradients in the aqueous sample and organic membrane phase. This work has important implications for the… (More)

The authors developed and analyzed a new method for an exact discretization of the spheroidal domains and for a construction of finite element spaces on such domains. Such method is based on a radial projection mapping defined on the ball into the cube in any space dimensions. The new method is applied on the Laplace–Beltrami equation and an eigenvalue… (More)

- W J Layton, A J Meir, Paul G Schmidt
- 2007

In this paper we describe and analyze a two-level method for discretizing the equations of stationary, viscous, incompressible magnetohydrodynamics. The MHD equations model the ow of a viscous, incompressible, electrically conducting uid, interacting with magnetic and electric elds. These arise in plasma physics, nuclear reactor technology, and geophysics.… (More)