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A new algorithm for solution of equations of MHD channel flows at moderate Hartmann numbers. (English) Zbl 0902.76058
Summary: An analytic finite element method (AFEM) is proposed for solving the governing equations of steady magnetohydrodynamic (MHD) duct flows. By the AFEM code one is able to calculate the flow field, the induced magnetic field, and the first partial derivatives of these fields. The process of the code generation is rather lengthy and complicated, therefore, to save space, the actual formulation is presented only for rectangular ducts. A distinguished feature of the AFEM code is the resolving capability of the high gradients near the walls without use of local mesh refinement. Results of traditional FEM, AFEM and finite difference method are compared with analytic results demonstrating the manifest superpriority of the AFEM code. The programs for the AFEM codes are implemented in GAUSS using traditional computer arithmetic and work in the range of low and moderate Hartmann numbers \(M<1000\).

MSC:
76M10 Finite element methods applied to problems in fluid mechanics
76W05 Magnetohydrodynamics and electrohydrodynamics
Software:
ELLPACK; GAUSS
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