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  • Optimization under Uncertainty of a Magnetohydrodynamics Generator

    Creator:
    Rajbhandari, Evan
    Abstract:
    Within this dissertation, we develop tools and techniques to demonstrate the feasibility of real-time optimization of a magnetohydrodynamics generator. To ease computational complexity, we work on the kinematic magnetohydrodynamic system, prescribing the fluid-flow and model the material response of the system through an updated Generalized Ohm’s law. We focus on...
    Resource Type:
    Dissertation
    Full Text:
    degree of Doctor of Philosophy in Mathematics presented on February 25, 2022. Title: Optimization under

  • Predicting Conductivity Within a Resistive Unsteady MHD Channel

    Creator:
    Rajbhandari, Evan
    Abstract:
    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...
    Resource Type:
    Technical Report
    Full Text:
    , estimating conductivity from the synthetic magnetic field using parameter optimization. Despite recovering

  • Stochastic Collocation Error Analysis Within a Kinematic Magnetohydrodynamics Framework

    Creator:
    Rajbhandari, Evan, Gibson, Nathan L., and Woodside, C. Rigel
    Abstract:
    We explore one numerical method for dealing with uncertainty quantification, stochastic collocation. We adapt this method for the uncertain kinematic magnetohydrodynamic system. We then demonstrate well-posedness of the uncertain forward problem. We also describe the method in detail, and perform an error analysis of the method, describing the necessary assumptions...
    Resource Type:
    Preprint
    Full Text:
    Center of Applied Mathematics And Information Technology, 2012. [5] M. Fortin, D. Boffi, and F. Brezzi

  • Quantifying uncertainty with stochastic collocation in the kinematic magentohydrodynamic framework

    Creator:
    Rajbhandari, Evan, Gibson, Nathan L., and Woodside, C. Rigel
    Abstract:
    We discuss an efficient numerical method for the uncertain kinematic magnetohydrodynamic system. We include aleatoric uncertainty in the parameters, and then describe a stochastic collocation method to handle this randomness. Numerical demonstrations of this method are discussed. We find that the shape of the parameter distributions affect not only the...
    Resource Type:
    Preprint
    Full Text:
    “combining coefficient” for anisotropic sparse grids. In Interdisciplinary Center of Applied Mathematics And

  • Parameter Estimation within a Kinematic Magnetohydrodynamics Framework

    Creator:
    Rajbhandari, Evan, Gibson, Nathan L., and Woodside, C. Rigel
    Abstract:
    We discuss the well-posedness of the forward problem for the magnetohydrodynamic system with the inclusion of the ion-slip parameter. We also demonstrate the convergence of a parameter estimation scheme. Focusing on power-generation, we implement and the validate a numerical model with an engineering multi-physics software, COMSOL, using ideal-power equations. We...
    Resource Type:
    Preprint
    Full Text:
    Magnetohydrodynamics Framework Evan Rajbhandari1, Nathan Gibson2, and C. Rigel Woodside3 1Department of Mathematics