In recent years, the discontinuous Galerkin (DG) method has been successfully applied to solving hyperbolic conservation laws. Due to its compactness, high order accuracy, and versatility, the DG method has been extensively applied to convection-diffusion problems. In this dissertation, a numerical package, texttt{PHORCE}, is introduced to solve a number of convection-diffusion problems in neutral fluids and plasmas. Unstructured grids are used in order to randomize grid errors, which is especially important for complex geometries. texttt{PHORCE} is written in texttt{C++} and fully parallelized using the texttt{MPI} library. Memory optimization has been considered in this work to achieve improved efficiency. DG algorithms for hyperbolic terms are well studied. However, an accurate and efficient diffusion solver still constitutes ongoing research, especially for a nodal representation of the discontinuous Galerkin (NDG) method. An affine reconstructed discontinuous Galerkin (aRDG) algorithm is developed in this work to solve the diffusive operator using an unstructured NDG method. Unlike other reconstructed/recovery algorithms, all computations can be performed on a reference domain, which promotes efficiency in computation and storage. In addition, to the best of the authors' knowledge, this is the first practical guideline that has been proposed for applying the reconstruction algorithm on a nodal discontinuous Galerkin method. TVB type and WENO type limiters are also studied to deal with numerical oscillations in regions with strong physical gradients in state variables. A high-order positivity-preserving limiter is also extended in this work to prevent negative densities and pressure. A new interface tracking method, mass of fluid (MOF), along with its bound limiter has been proposed in this work to compute the mass fractions of different fluids over time. Hydrodynamic models, such as Euler and Navier-Stokes equations, and plasma models, such as ideal-magnetohydrodynamics (MHD) and two-fluid plasma equations, are studied and benchmarked with various applications using this DG framework. Numerical computations of Rayleigh-Taylor instability growth with experimentally relevant parameters are performed using hydrodynamic and MHD models on planar and radially converging domains. Discussions of the suppression mechanisms of Rayleigh-Taylor instabilities due to magnetic fields, viscosity, resistivity, and thermal conductivity are also included. This work was partially supported by the US Department of Energy under grant number DE-SC0016515. The author acknowledges Advanced Research Computing at Virginia Tech for providing computational resources and technical support that have contributed to the results reported within this work. URL: http://www.arc.vt.edu / Doctor of Philosophy / High-energy density (HED) plasma science is an important area in studying astrophysical phenomena as well as laboratory phenomena such as those applicable to inertial confinement fusion (ICF). ICF plasmas undergo radial compression, with an aim of achieving fusion ignition, and are subject to a number of hydrodynamic instabilities that can significantly alter the implosion and prevent sufficient fusion reactions. An understanding of these instabilities and their mitigation mechanisms is important allow for a stable implosion in ICF experiments. This work aims to provide a high order accurate and robust numerical framework that can be used to study these instabilities through simulations. The first half of this work aims to provide a detailed description of the numerical framework, texttt{PHORCE}. texttt{PHORCE} is a high order numerical package that can be used in solving convection-diffusion problems in neutral fluids and plasmas. Outstanding challenges exist in simulating high energy density (HED) hydrodynamics, where very large gradients exist in density, temperature, and transport coefficients (such as viscosity), and numerical instabilities arise from these region if there is no intervention. These instabilities may lead to inaccurate results or cause simulations to fail, especially for high-order numerical methods. Substantial work has been done in texttt{PHORCE} to improve its robustness in dealing with numerical instabilities. This includes the implementation and design of several high-order limiters. An novel algorithm is also proposed in this work to solve the diffusion term accurately and efficiently, which further enriches the physics that texttt{PHORCE} can investigate. The second half of this work involves rigorous benchmarks and experimentally relevant simulations of hydrodynamic instabilities. Both advection and diffusion solvers are well verified through convergence studies. Hydrodynamic and plasma models implemented are also validated against results in existing literature. Rayleigh-Taylor instability growth with experimentally relevant parameters are performed on both planar and radially converging domains. Although this work is motivated by physics in HED hydrodynamics, the emphasis is placed on numerical models that are generally applicable across a wide variety of fields and disciplines.

A careful study of plasma-material interactions is essential to understand and improve the operation of devices where plasma contacts a wall such as plasma thrusters, fusion devices, spacecraft-environment interactions, to name a few. This work aims to advance our understanding of fundamental plasma processes pertaining to plasma-material interactions, sheath physics, and kinetic instabilities through theory and novel numerical simulations. Key contributions of this work include (i) novel continuum kinetic algorithms with novel boundary conditions that directly discretize the Vlasov/Boltzmann equation using the discontinuous Galerkin method, (ii) fundamental studies of plasma sheath physics with collisions, ionization, and physics-based wall emission, and (iii) theoretical and numerical studies of the linear growth and nonlinear saturation of the kinetic Weibel instability, including its role in plasma sheaths. The continuum kinetic algorithm has been shown to compare well with theoretical predictions of Landau damping of Langmuir waves and the two-stream instability. Benchmarks are also performed using the electromagnetic Weibel instability and excellent agreement is found between theory and simulation. The role of the electric field is significant during nonlinear saturation of the Weibel instability, something that was not noted in previous studies of the Weibel instability. For some plasma parameters, the electric field energy can approach magnitudes of the magnetic field energy during the nonlinear phase of the Weibel instability. A significant focus is put on understanding plasma sheath physics which is essential for studying plasma-material interactions. Initial simulations are performed using a baseline collisionless kinetic model to match classical sheath theory and the Bohm criterion. Following this, a collision operator and volumetric physics-based source terms are introduced and effects of heat flux are briefly discussed. Novel boundary conditions are developed and included in a general manner with the continuum kinetic algorithm for bounded plasma simulations. A physics-based wall emission model based on first principles from quantum mechanics is self-consistently implemented and demonstrated to significantly impact sheath physics. These are the first continuum kinetic simulations using self-consistent, wall emission boundary conditions with broad applicability across a variety of regimes. / Ph. D. / An understanding of plasma physics is vital for problems on a wide range of scales: from large astrophysical scales relevant to the formation of intergalactic magnetic fields, to scales relevant to solar wind and space weather, which poses a significant risk to Earth’s power grid, to design of fusion devices, which have the potential to meet terrestrial energy needs perpetually, and electric space propulsion for human deep space exploration. This work aims to further our fundamental understanding of plasma dynamics for applications with bounded plasmas. A comprehensive understanding of theory coupled with high-fidelity numerical simulations of fundamental plasma processes is necessary, this then can be used to improve improve the operation of plasma devices. There are two main thrusts of this work. The first thrust involves advancing the state-of-the-art in numerical modeling. Presently, numerical simulations in plasma physics are typically performed either using kinetic models such as particle-in-cell, where individual particles are tracked through a phase-space grid, or using fluid models, where reductions are performed from kinetic physics to arrive at continuum models that can be solved using well-developed numerical methods. The novelty of the numerical modeling is the ability to perform a complete kinetic calculation using a continuum description and evolving a complete distribution function in phase-space, thus resolving kinetic physics with continuum numerics. The second thrust, which is the main focus of this work, aims to advance our fundamental understanding of plasma-wall interactions as applicable to real engineering problems. The continuum kinetic numerical simulations are used to study plasma-material interactions and their effects on plasma sheaths. Plasma sheaths are regions of positive space charge formed everywhere that a plasma comes into contact with a solid surface; the charge inequality is created because mobile electrons can quickly exit the domain. A local electric field is self-consistently created which accelerates ions and retards electrons so the ion and electron fluxes are equalized. Even though sheath physics occurs on micro-scales, sheaths can have global consequences. The electric field accelerates ions towards the wall which can cause erosion of the material. Another consequence of plasma-wall interaction is the emission of electrons. Emitted electrons are accelerated back into the domain and can contribute to anomalous transport. The novel numerical method coupled with a unique implementation of electron emission from the wall is used to study plasma-wall interactions. While motivated by Hall thrusters, the applicability of the algorithms developed here extends to a number of other disciplines such as semiconductors, fusion research, and spacecraft-environment interactions.

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La projection par plasma d'arc de suspension permet d'obtenir des revêtements finement structurés à gradients de propriétés qui répondent aux besoins, par exemple, des applications photocatalytiques, les piles à combustible à oxyde solide ou les revêtements de barrière thermique. Cependant, les torches à plasma, même alimentées par dessources de courant continu régulé, génèrent des jets de plasma fortement fluctuants. Ces instabilités causent des variations importantes dans les transferts thermiques et dynamiques des particules, ce qui diminue la fiabilité et la reproductibilité de la méthode. Par conséquent, des efforts particuliers doivent être faits pour améliorer la projectionpar plasma d'arc de suspension et, ainsi, les propriétés des revêtements. Depuis de nombreuses années, la recherche s'est concentrée sur l'amélioration des transferts de chaleur et de quantité de mouvement entre la matière et le plasma au moyen de la mise au point de nouvelles torches et la réduction des instabilités de l'arc. Cette thèse présenteune nouvelle approche pour la projection par plasma d'arc de suspension. L'étude approfondie des instabilités du plasma sont réalisées ce qui conduit à la production du jet laminaire de plasma pulsé caractérisé par une forte modulation de l'enthalpie spécifique. Ces oscillations régulières de plasma sont associées à l'injection de la suspensionsynchronisée, ce qui est réalisé à l'aide de l'impression à jet d'encre déclenchée par le signal de tension d'arc. Les résultats sont évalués par le système d'imagerie résolue en temps et la spectroscopie d'émission optique résolue en temps. Cette nouvelle méthode offre la possibilité de contrôler les transferts de chaleur et de quantité de mouvemententre les particules et le plasma. / Suspension plasma spraying permits to elaborate finely structured coatings with graded properties which address the needs, for example, in the photocatalytic applications, the solid oxide fuels or the thermal barrier coatings. However, the plasma torches, even powered by dc regulated sources, generate highly fluctuating plasma jets. These instabilities result in large variations in dynamic and heat transfers to particles, what decreases the reproducibility and reliability of the method. Consequently, the special efforts have to be devoted to ameliorate the suspension plasma spraying method and, thus, the properties of the coatings. In recent years, the research has been focused on the improvement of heat and momentum transfers between material and plasma by means of the development of new non-conventional torches and the reduction of arc instabilities. The following dissertation presents a new approach to the suspension plasma spraying. The profound studies of the plasma instabilities are performed, what leads to the production of the pulsed laminar plasma jet characterized by high modulation of the specific enthalpy. These regular plasma oscillations are combined with phased injection of suspension, what is achieved by using the ink-jet printer triggered by the arc voltage signal. The results are evaluated by time-resolved imaging system and the time-resolved emission optical spectroscopy. This new method presents the possibility to control heat and momentum transfers between the particles and the plasma.

The common observation that the onset of a core MARFE (edge localized, poloidally asymmetric, highly radiating region) is followed immediately by a High-to-Low confinement mode transition in DIII-D was investigated by comparing a theoretical prediction of the threshold non-radiative power across the separatrix needed to maintain H-mode with an experimental determination of the non-radiative power flowing across the separatrix. It was found that in three shots with continuous gas fueling that the increased neutral influx associated with the MARFE formation caused a sharp increase in the predicted threshold non-radiative power crossing the separatrix that was required for the plasma to remain in H-mode to a value comparable to the experimental power crossing the separatrix, indicating a theoretical prediction of a H-L transition in agreement with experimental observation.