Discontinuous Galerkin Studies of Collisional Dynamics in Continuum-Kinetic Plasma
| dc.contributor.author | Rodman, John Morgan | en |
| dc.contributor.committeechair | Srinivasan, Bhuvana | en |
| dc.contributor.committeemember | Scales, Wayne A. | en |
| dc.contributor.committeemember | Adams, Colin | en |
| dc.contributor.committeemember | Warburton, Timothy | en |
| dc.contributor.department | Aerospace and Ocean Engineering | en |
| dc.date.accessioned | 2025-01-25T09:00:12Z | en |
| dc.date.available | 2025-01-25T09:00:12Z | en |
| dc.date.issued | 2025-01-24 | en |
| dc.description.abstract | Numerical investigations of collisional physics have historically been impeded by the issue of computational expense. While the continuum-kinetic Vlasov-Maxwell-Fokker-Planck system is well-established in theory and has been used as the basis for many approximate fluid equations, simulations utilizing the distribution function are relatively uncommon, due primarily to the high dimensionality of the problem. However, advances in numerical methods are steadily making these models more accessible. In this work, we utilize the Gkeyll framework, which applies a novel, highly efficient discontinuous Galerkin (DG) finite element method to the Vlasov-Maxwell-Fokker-Planck system. We first investigate the Rayleigh-Taylor (RT) instability in a neutral gas in regimes of finite collisionality which are inaccessible to the fluid codes that are traditionally applied to this instability. Utilizing a spatially constant, finite collision frequency, we demonstrate the ability of the Vlasov-Boltzmann model to approach the fluid result at high collision frequency while also accessing a regime of intermediate collisionality in which the RT instability deviates greatly from classic fluid behavior. We then extend upon this finding by choosing a collision frequency that varies spatially, resulting in new dynamics with asymmetric diffusion affecting the development of the RT instability. Having demonstrated the utility of collisional kinetic modeling even in the simple case of a neutral gas with a basic collision operator, we transition to development and implementation of a fully-conservative, recovery-based DG algorithm for the full nonlinear Rosenbluth/Fokker-Planck collision operator (FPO). Details of the novel recovery scheme for the cross-derivatives and conservation enforcement are presented, and we show that the scheme converges and exhibits stability criteria as expected. Finally, the FPO is applied to test cases that demonstrate the importance of accurate handling of the velocity-dependent collision frequency as compared to an approximate model. | en |
| dc.description.abstractgeneral | Under the right conditions, the electrons and ions that comprise the particles in a gas separate, or ionize, forming a plasma. Plasma is the most common state of matter in the universe, existing at a wide range of scales. Whether concerning a supernova, the solar wind, a plume of material ablated by a laser, or a nuclear fusion reactor, all of these plasmas are governed by the same set of rules, with the main differences being which length and time scales are relevant. Understanding the dynamics of these collections of ionized particles offers a unique challenge, as particles interact not only by colliding with one another but through longer-range electromagnetic interactions. A number of methods exist for modeling plasmas, and one must choose which of the many scales in the plasma are relevant in order to make the best choice of model. In this work, we apply the continuum-kinetic method, which captures the statistical effect of individual particle motions while avoiding the noise that arises when tracking individual particles directly. Kinetic methods are not applied nearly as often as fluid methods, primarily because of the computational expense involved in resolving the wide range of scales and accounting for quantities that evolve as a function of both position and velocity. However, recent advances in numerical methods have made continuum-kinetic methods much more accessible. This work utilizes the Gkeyll code framework, which applies a discontinuous Galerkin method, to simulate plasma with a continuum-kinetic model. We begin by considering the Rayleigh-Taylor (RT) instability, which occurs when a heavy fluid is balanced atop a lighter fluid and perturbed, resulting in fluid mixing. The RT instability is ubiquitous in nature and is commonly modeled with fluid methods that assume particle collide with one another with effectively infinite frequency. With the continuum-kinetic method, we demonstrate that situations arise where the collision frequency is finite but the RT instability still grows. In these regimes, the instability growth is no longer well-described by fluid methods, and a kinetic model must be applied to accurately predict its evolution. Following this, we introduce an algorithm that utilizes a novel discontinuous Galerkin (DG) method to model one of the most complex and accurate collision operators for plasmas: the Fokker-Planck operator (FPO). The FPO is notoriously difficult to implement numerically and computationally expensive due to its nonlinear nature, so simulations generally utilize approximate forms rather than the full operator. By applying this DG method, we are able to ensure the numerical FPO implementation maintains many of the desirable properties of the original model while running highly efficiently. We conclude by verifying that the code is stable and highly accurate while reproducing expected results and improvements over simplified collision models. | en |
| dc.description.degree | Doctor of Philosophy | en |
| dc.format.medium | ETD | en |
| dc.identifier.other | vt_gsexam:42153 | en |
| dc.identifier.uri | https://hdl.handle.net/10919/124380 | en |
| dc.language.iso | en | en |
| dc.publisher | Virginia Tech | en |
| dc.rights | Creative Commons Attribution 4.0 International | en |
| dc.rights.uri | http://creativecommons.org/licenses/by/4.0/ | en |
| dc.subject | plasma | en |
| dc.subject | discontinuous Galerkin | en |
| dc.subject | collisions | en |
| dc.subject | continuum kinetic | en |
| dc.title | Discontinuous Galerkin Studies of Collisional Dynamics in Continuum-Kinetic Plasma | en |
| dc.type | Dissertation | en |
| thesis.degree.discipline | Aerospace Engineering | en |
| thesis.degree.grantor | Virginia Polytechnic Institute and State University | en |
| thesis.degree.level | doctoral | en |
| thesis.degree.name | Doctor of Philosophy | en |
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