Type
Text
Type
Dissertation
Advisor
Samulyak, Roman | Glimm, James | Jiao, Xiangmin | Calder, Alan.
Date
2013-12-01
Keywords
Mathematics | embedded boundary method, front tracking, Lagrangian particle method, magnetohydrodynamics
Department
Department of Applied Mathematics and Statistics.
Language
en_US
Source
This work is sponsored by the Stony Brook University Graduate School in compliance with the requirements for completion of degree.
Identifier
http://hdl.handle.net/11401/77643
Publisher
The Graduate School, Stony Brook University: Stony Brook, NY.
Format
application/pdf
Abstract
New mesh and meshless algorithms for elliptic boundary and elliptic interface problems have been developed. By utilizing the embedded boundary method, a mesh based algorithm to solve elliptic interface problem is implemented as an extension of hybrid Eulerian-Lagrangian hydrodynamic library FronTier which employs the method of front tracking for interface propagation and this implementation is parallelized for distributed memory clusters. The use of embedded boundary method supports arbitrary discontinuities of density and other physics properties across the interfaces and significantly improves methods that smear interface discontinuities across several grid cells. This code has been applied to process simulation for heat transfer problem, stefan problem and magnetohydrodynamics at low magnetic Reynolds number. To handle problems brought by the complexity of interfaces, algorithms for solving elliptic boundary and elliptic interface problems have been proposed based on meshless particle-based method. The typical feature of the elliptic interface problem is the presence of a geometrically complex internal boundary across which material properties or solutions rapidly change. The main motivation for the development of particle-based methods for elliptic problems is to carry out numerical simulation of free surface of multiphase systems described by coupled hyperbolic and elliptic equations. A Lagrangian particle technique, smoothed particle hydrodynamics(SPH) has been implemented and tested. To overcome the drawbacks of poor numerical accuracy of SPH, another Lagrangian particle technique with local polynomial fitting has been developed and implemented. All the implementation is fully parallelized. The current work deals with methods for elliptic components of coupled systems. And, the developed elliptic methods, if used independently, also favorably compare to unstructured finite element methods that require mesh generation and depend on the mesh quality. Currently, a second order accurate algorithm has been used and higher order discretization is also possible. | 112 pages
Recommended Citation
Guo, Tongfei, "Scalable Particle and Mesh Algorithms for Elliptic Components of Multiphase Problems" (2013). Stony Brook Theses and Dissertations Collection, 2006-2020 (closed to submissions). 3437.
https://commons.library.stonybrook.edu/stony-brook-theses-and-dissertations-collection/3437