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Numerical methods to analyze and post-process solutions of plasma and gas dynamics problems

Terrab, Soraya
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Ryan, Jennifer K.
Wu Fung, Samy
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2025
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2025 - Mines Theses & Dissertations
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Terrab_mines_0052E_13034.pdf
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  • Embargoed until 2026-11-11
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https://hdl.handle.net/11124/181124
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2026-11-11
Abstract
Numerical methods to analyze and solve solutions to PDEs continue to evolve leading to a vast array of numerical techniques from scientific computing, uncertainty quantification, signal processing, and machine learning. Rooted in fundamental physics and constitutive relations, these tools are essential for in-depth numerical data extraction and analysis. In this doctoral work, we leverage the dispersion relation to: 1) calculate the growth rate of a collisionless plasma, described by the Vlasov-Poisson system for particle-in-cell plasma dynamics, and apply dimension reduction, and 2) analyze and mitigate spurious oscillations in hyperbolic PDEs, particularly the Euler equations for inviscid, compressible gas dynamics, through the use of post-processing filtering. For the plasma dynamics problem, we use active subspace analysis to analyze the key parameter contributions in the growth rate of steady-state plasma distributions. The global sensitivity analysis sheds light on the induced uncertainty due to perturbations in a collisionless plasma. As for hyperbolic PDEs, we use the Discontinuous Galerkin (DG) method, which we further improve by combining discontinuity detection and post-processing filtering to resolve the solution about the shock waves that arise in Euler equations. We present a hybrid filter for discontinuities using Smoothness-Increasing Accuracy-Conserving (SIAC) and data-driven techniques, which reduces the error about discontinuities by applying a convolutional neural network trained to resolve SIAC-filtered discontinuity data. In addition, we examine the effectiveness of the SIAC filter for time-stepping schemes using spectral analysis of the numerical dispersion to limit the spread of spurious oscillations in time for discontinuous solutions.
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