Finite element analysis of magnetohydrodynamic pipe flow

摘要

This paper deals with magnetohydrodynamic flows in pipes with arbitrary cross-section and arbitrary wall conductivities under the influence of a transverse magnetic field. The equations studied are of considerable practical interest since they model induction flow meters, electromagnetic pumps, magnetic propulsion devices and generators and have application in medicine, in power generation and in nuclear reactor technology. We are primarily interested in the questions of existence, uniqueness and finite element approximation of solutions to the equations of steady-state magnetohydrodynamics with arbitrary boundary conditions which describe this phenomenon. We derive error estimates for the approximate solution and show that one obtains optimal accuracy when using the finite element method to construct approximate solutions. We illustrate these results with some numerical experiments.