Finite element approximation of biharmonic mathematical model for MHD flow using /spl Psi/-an approach

A generalized mathematical model describing the dynamics of magnetic field influence on a conducting liquid in a square cavity is presented. A method involving a biharmonic mathematical model with stream function /spl Psi/, and the magnetic potential A was used. The Galerkin method was applied to so...

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Bibliographic Details
Published in:IEEE transactions on magnetics 2000-07, Vol.36 (4), p.1313-1318
Main Authors: Krzeminski, S.K., Smialek, M., Wlodarczyk, M.
Format: Article
Language:English
Subjects:
Boundary conditions
Finite element methods
Magnetic field measurement
Magnetic fields
Magnetic liquids
Magnetohydrodynamics
Mathematical model
Moment methods
Newton method
Nonlinear equations
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Summary:A generalized mathematical model describing the dynamics of magnetic field influence on a conducting liquid in a square cavity is presented. A method involving a biharmonic mathematical model with stream function /spl Psi/, and the magnetic potential A was used. The Galerkin method was applied to solve a system of two variational identities. A numerical finite element algorithm based on the second order elements was developed. In the algorithm the Newton-Raphson method is used to solve the resulting nonlinear system. Numerical experiments with different Reynolds (R/sub e/, R/sub m/) and Hartmann (H/sub /spl alpha//) numbers were presented in graphical form.
ISSN:0018-9464
1941-0069
DOI:10.1109/20.877681