Finite element analysis of MHD laminar flow using object-oriented technology
Stanisław Krzemiński , Michał Śmiałek , Maciej Włodarczyk
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.
|Journal series||European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2000|
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