A fourth-order finite volume algorithm with adaptive mesh refinement in space and time for multi-fluid plasma modeling

Polak, Scott E., author
Gao, Xinfeng, advisor
Guzik, Stephen, committee member
Tomasel, Fernando, committee member
Ghosh, Debojyoti, committee member
Bangerth, Wolfgang, committee member
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Improving our fundamental understanding of plasma physics using numerical methods is pivotal to the advancement of science and the continual development of cutting-edge technologies such as nuclear fusion reactions for energy production or the manufacturing of microelectronic devices. An elaborate and accurate approach to modeling plasmas using computational fluid dynamics (CFD) is the multi-fluid method, where the full set of fluid mechanics equations are solved for each species in the plasma simultaneously with Maxwell's equations in a coupled fashion. Nevertheless, multi-fluid plasma modeling is inherently multiscale and multiphysics, presenting significant numerical and mathematical stiffness. This research aims to develop an efficient and accurate multi-fluid plasma model using higher-order, finite-volume, solution-adaptive numerical methods. The algorithm developed herein is verified to be fourth-order accurate for electromagnetic simulations as well as those involving fully-coupled, multi-fluid plasma physics. The solutions to common plasma test problems obtained by the algorithm are validated against exact solutions and results from literature. The algorithm is shown to be robust and stable in the presence of complex solution topology and discontinuities, such as shocks and steep gradients. The optimizations in spatial discretization provided by the fourth-order algorithm and adaptive mesh refinement are demonstrated to improve the solution time by a factor of 10 compared to lower-order methods on fixed-grid meshes. This research produces an advanced, multi-fluid plasma modeling framework which allows for studying complex, realistic plasmas involving collisions and practical geometries.
2022 Spring.
Includes bibliographical references.
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finite-volume method
adaptive mesh refinement
numerical model
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