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    A Monolithic Finite Element Formulation for Magnetohydrodynamics Involving a Compressible Fluid

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    Gupta, Adhip
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    Abstract
    This work develops a new monolithic finite-element-based strategy for Magnetohydrodynamics (MHD) involving a compressible fluid based on a continuous velocity-pressure formulation. The entire formula- tion is within a nodal finite element framework, and is directly in terms of physical variables. The exact linearization of the variational formulation ensures a quadratic rate of convergence in the vicinity of the solution. Both steady-state and transient formulations are presented for two- and three-dimensional flows. Several benchmark problems are presented, and comparisons are carried out against analytical solutions, experimental data, or against other numerical schemes for MHD. We show a good coarse-mesh accuracy and robustness of the proposed strategy, even at high Hartmann numbers.
    URI
    https://etd.iisc.ac.in/handle/2005/6188
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    • Mechanical Engineering (ME) [386]

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