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dc.contributor.advisorAlexeev, Alexander
dc.contributor.authorVasyliv, Yaroslav V.
dc.date.accessioned2016-01-07T17:38:15Z
dc.date.available2016-01-07T17:38:15Z
dc.date.created2015-12
dc.date.issued2015-11-17
dc.date.submittedDecember 2015
dc.identifier.urihttp://hdl.handle.net/1853/54425
dc.description.abstractIn meshfree methods, partial differential equations are solved on an unstructured cloud of points distributed throughout the computational domain. In collocated meshfree methods, the differential operators are directly approximated at each grid point based on a local cloud of neighboring points. The set of neighboring nodes used to construct the local approximation is determined using a variable search radius. The variable search radius establishes an implicit nodal connectivity and hence a mesh is not required. As a result, meshfree methods have the potential flexibility to handle problem sets where the computational grid may undergo large deformations as well as where the grid may need to undergo adaptive refinement. In this work we develop the sharp interface formulation of the immersed boundary method for collocated meshfree approximations. We use the framework to implement three meshfree methods: General Finite Differences (GFD), Smoothed Particle Hydrodynamics (SPH), and Moving Least Squares (MLS). We evaluate the numerical accuracy and convergence rate of these methods by solving the 2D Poisson equation. We demonstrate that GFD is computationally more efficient than MLS and show that its accuracy is superior to a popular corrected form of SPH and comparable to MLS. We then use GFD to solve several canonic steady state fluid flow problems on meshfree grids generated using uniform and variable radii Poisson disk algorithm.
dc.format.mimetypeapplication/pdf
dc.language.isoen_US
dc.publisherGeorgia Institute of Technology
dc.subjectCollocated meshfree methods
dc.subjectGeneral finite differences
dc.subjectSharp interface
dc.subjectImmersed boundary method
dc.subjectPoisson disk sampling
dc.subjectMoving least squares
dc.subjectSmoothed particle hydrodynamics
dc.titleDevelopment of general finite differences for complex geometries using immersed boundary method
dc.typeThesis
dc.description.degreeM.S.
dc.contributor.departmentMechanical Engineering
thesis.degree.levelMasters
dc.contributor.committeeMemberChow, Edmond
dc.contributor.committeeMemberKumar, Satish
dc.date.updated2016-01-07T17:38:15Z


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