Finite element analysis of MHD laminar flow using object-oriented technology

Stanisław Krzemiński , Michał Śmiałek , Maciej Włodarczyk

Abstract

The paper presents a numerical solution of a standard Couette flow problem extended by adding the influence of the magnetic field. To describe the coupled velocity field and magnetic field, a method with the hydrodynamic and magnetic vector potentials (Ψ,A) and vorticity vector (ξ) is used. The Galerkin method is used to formulate a generalized mathematical model. Based on this mathematical formulation, a non-linear algebraic system of equations is derived by using finite elements. To solve this non-linear system the Newton-Raphson method is applied. The algorithm's iteration Jacobian is constructed using smaller objects included in the discrete formulation. Finally, an object-oriented model based on the numerical formulation is presented. This model describes the software design solutions used to produce the final simulator. The numerical results obtained using this simulator confirm correctness an effectiveness of the developed algorithm. The results are presented as a set of diagrams showing velocity and magnetic field distribution in a channel cross-section for a square and triangular cavity.

Author Stanisław Krzemiński (FoEE)
Stanisław Krzemiński,,
- Faculty of Electrical Engineering
, Michał Śmiałek (FoEE / ITEEMIS)
Michał Śmiałek,,
- The Institute of the Theory of Electrical Engineering, Measurement and Information Systems
, Maciej Włodarczyk (WUT)
Maciej Włodarczyk,,
- Warsaw University of Technology
Journal seriesEuropean Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2000
Issue year2000
Languageen angielski
Score (nominal)0
Score sourcejournalList
Publication indicators Scopus Citations = 0
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