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Predicting Conductivity Within a Resistive Unsteady MHD Channel Public Deposited

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  • The theory behind magnetohydrodynamics (MHD) is utilized to present a 3-D solution to how the induced magnetic field changes with respect to time. Several MHD-based assump- tions are made to simplify the coupling of Maxwell’s equations with two constitutive laws and Ohm’s law. The velocity field is assumed to be known to reduce computation complexi- ties. A non-uniform approach to cylindrical mesh discretization is also presented, attempting to prevent a clustering of nodes near the origin. A numerical approximation to the solu- tion within the discretized channel is then found, using a forward-in-time algorithm, and a centered-in-space approximation to spatial derivatives. This model is used to generate some data with known conductivity. Gaussian noise with varying noise levels is then added, and non-linear least squares is employed to solve the inverse problem, estimating conductivity from the synthetic magnetic field using parameter optimization. Despite recovering the true parameters in the absence of noise, even a slight perturbation in the given data resulted in convergence to completely incorrect parameter values, implying that the inverse problem is not stable.
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