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Scalable Particle and Mesh Algorithms for Elliptic Components of Multiphase Problems

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dc.contributor.advisor Samulyak, Roman en_US
dc.contributor.author Guo, Tongfei en_US
dc.contributor.other Department of Applied Mathematics and Statistics. en_US
dc.date.accessioned 2017-09-20T16:53:10Z
dc.date.available 2017-09-20T16:53:10Z
dc.date.issued 2013-12-01
dc.identifier.uri http://hdl.handle.net/11401/77643 en_US
dc.description 112 pg. en_US
dc.description.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. en_US
dc.description.sponsorship This work is sponsored by the Stony Brook University Graduate School in compliance with the requirements for completion of degree. en_US
dc.format Monograph en_US
dc.format.medium Electronic Resource en_US
dc.language.iso en_US en_US
dc.publisher The Graduate School, Stony Brook University: Stony Brook, NY. en_US
dc.subject.lcsh Mathematics en_US
dc.subject.other embedded boundary method, front tracking, Lagrangian particle method, magnetohydrodynamics en_US
dc.title Scalable Particle and Mesh Algorithms for Elliptic Components of Multiphase Problems en_US
dc.type Dissertation en_US
dc.mimetype Application/PDF en_US
dc.contributor.committeemember Glimm, James en_US
dc.contributor.committeemember Jiao, Xiangmin en_US
dc.contributor.committeemember Calder, Alan. en_US

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