자료유형  

 학위논문

Control Number  

0016935197

International Standard Book Number  

9798380713535

Dewey Decimal Classification Number  

515.353

Main Entry-Personal Name  

Redle, Michael Thomas.

Publication, Distribution, etc. (Imprint  

[S.l.] : North Carolina State University., 2023

Publication, Distribution, etc. (Imprint  

Ann Arbor : ProQuest Dissertations & Theses, 2023

Physical Description  

1 online resource(181 p.)

General Note  

Source: Dissertations Abstracts International, Volume: 85-05, Section: B.

General Note  

Advisor: Frohlich, Carla;Chertock, Alina.

Dissertation Note  

Thesis (Ph.D.)--North Carolina State University, 2023.

Restrictions on Access Note  

This item must not be sold to any third party vendors.

Summary, Etc.  

요약We are interested in studying systems of conductive fluids, such as salt water, plasmas, and liquid metals, when in the presence of magnetic field, otherwise referred to magnetohydrodynamics or MHD. These systems - descriptive of many applications within astrophysics, geophysics, and engineering - are constrained by the infamous divergence-free condition of the magnetic field. This constraint is physically exact, as magnetic monopoles have not been observed in nature, and must be treated as such on a numerical level as well. If otherwise neglected, this constraint may lead to spurious oscillations or nonphysical solutions - even when using other methods known to accurately capture systems without this constraint. Therefore, a proper construction of this identically-zero divergence is vital at a discrete level. In this work, we develop a novel second-order method based on the path-conservative central upwind scheme that not only treats this condition exactly, but additionally is computed on an unstaggered grid without the need of Riemann solvers. This method provably preserves the local divergence-free condition, and has been successfully tested on several numerical benchmarks for both ideal and shallow water MHD.In addition to forming a robust method treating the divergence constraint, we turn our focus and study multiscale phenomena of the shallow water MHD system, in which we now consider effects due to rotation and a nonflat bottom topography. This system admits a number of physically-relevant steady-state solutions, in addition to relevant small perturbations of these equilibria. We thus develop a well-balanced extension of the previously discussed divergence-free method to capture these steady-states exactly, which as a result, provides the added benefit of capturing small perturbations on a coarser grid. This new method maintains the properties of the previously discussed divergence-free scheme, but also exactly preserves still-water and moving-water equilibrium in both 1-D and 2-D. This method has additionally been tested successfully on a number of examples, returning non-oscillatory, high-resolution solutions.Lastly, we look at astrophysical contexts of MHD, in which our overall goal is to analyze the effects of a 3-D magnetic field on neutrino-driven star explosions. In pursuit of answers on this front, we must form a number of data analysis and visualization tools for the 3-D solutions obtained through an MHD and neutrino transport code nicknamed ELEPHANT. The formulation of these analysis tools, along with the corresponding visualizations, are presented using three variants of a single 20M⊙initial star.

Subject Added Entry-Topical Term  

Finite volume method.

Subject Added Entry-Topical Term  

Entropy.

Subject Added Entry-Topical Term  

Magnetic fields.

Subject Added Entry-Topical Term  

Explosions.

Subject Added Entry-Topical Term  

Electromagnetics.

Subject Added Entry-Topical Term  

Mathematics.

Added Entry-Corporate Name  

North Carolina State University.

Host Item Entry  

Dissertations Abstracts International. 85-05B.

Host Item Entry  

Dissertation Abstract International

Electronic Location and Access  

로그인을 한후 보실 수 있는 자료입니다.

Control Number  

joongbu:642893