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A monolithic finite-element formulation for magnetohydrodynamics

Nandy, Arup and Jog, C S (2018) A monolithic finite-element formulation for magnetohydrodynamics. In: SADHANA-ACADEMY PROCEEDINGS IN ENGINEERING SCIENCES, 43 (9).

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Official URL: https://dx.doi.org/10.1007/s12046-018-0905-z

Abstract

This work develops a new monolithic strategy for magnetohydrodynamics based on a continuous velocity-pressure formulation. The magnetic field is interpolated in the same way as the velocity field, and the entire formulation is within a nodal finite-element framework. The velocity and pressure interpolations are chosen so that they satisfy the Babuska-Brezzi (BB) conditions. In most of the existing formulations, a stabilized formulation is used that requires a stabilization term, and some associated mesh-dependent parameters that need to be adjusted. In contrast, no such parameters need to be adjusted in the current formulation, making it more user-friendly and robust. Both transient and steady-state formulations are developed for two- and three-dimensional geometries. An exact linearization of the monolithic strategy ensures that rapid (quadratic) convergence is achieved within each time (or load) step, while the stable nature of the interpolations used ensures that no instabilities arise in the solution. An existing analytical solution is corrected. The coarse mesh accuracy is shown to be better compared with other existing strategies in several benchmark problems, showing that the developed formulation is both robust and efficient.

Item Type: Journal Article
Additional Information: Copyright of this article belong to SPRINGER INDIA, 7TH FLOOR, VIJAYA BUILDING, 17, BARAKHAMBA ROAD, NEW DELHI, 110 001, INDIA
Department/Centre: Division of Mechanical Sciences > Mechanical Engineering
Depositing User: Id for Latest eprints
Date Deposited: 16 Aug 2018 16:04
Last Modified: 16 Aug 2018 16:04
URI: http://eprints.iisc.ac.in/id/eprint/60435

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