Abstract
Starting from the basic and general approach founded on the coupling between the Maxwell and the Navier- Stokes equations, the authors review some physical and mathematical models that are currently used in the aerospace engineering community for representing the behavior of electrically conducting flows subject to electromagnetic fields. Then, they present four different numerical methods for solving the magnetofluid dynamics equations in different formulations and for different magnetic Reynolds number regimes. For the sake of simplicity, the attention is focused on one-dimensional cases. Finally, numerical results obtained using the above mentioned numerical techniques on a magnetofluid dynamics shock-tube problem are compared and discussed
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