2026-09-18T20:53:09Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/627122022-01-13T07:54:11Zcom_1721.1_7582com_1721.1_7581col_1721.1_131023
Ahmed F. Ghoniem.
Vasilyeva, Anna, S.M. Massachusetts Institute of Technology
Massachusetts Institute of Technology. Dept. of Aeronautics and Astronautics.
Massachusetts Institute of Technology. Department of Aeronautics and Astronautics
2011-05-09T15:23:53Z
2011-05-09T15:23:53Z
2010
2010
http://hdl.handle.net/1721.1/62712
714615024
Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2010.
Cataloged from PDF version of thesis.
Includes bibliographical references (p. 58-60).
The numerical approximation of the Poisson equation can often be found as a subproblem to many more complex computations. In the case of Lagrangian approaches of flow equations, the Poisson equation often needs to be solved on an irregular point distribution. Currently, mainly unstructured mesh-based approaches are used. Meshfree methods present a way to approximate differential operators on unstructured point clouds without the need for mesh generation. In this thesis, a 3d meshfree finite difference Poisson solver is presented. Its performance has been studies based on numerical convergence, parallel efficiency, and computational cost. Practical application of the solver is presented in a simulation of a potential flow field in a wall-bounded domain.
by Anna Vasilyeva.
S.M.
60 p.
eng
Massachusetts Institute of Technology
M.I.T. theses are protected by
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http://dspace.mit.edu/handle/1721.1/7582
Aeronautics and Astronautics.
A meshfree method for the Poisson equation with 3D wall-bounded flow application
Mesh free method for the Poisson equation with 3D wall-bounded flow application
Thesis
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<Abstract>The numerical approximation of the Poisson equation can often be found as a subproblem to many more complex computations. In the case of Lagrangian approaches of flow equations, the Poisson equation often needs to be solved on an irregular point distribution. Currently, mainly unstructured mesh-based approaches are used. Meshfree methods present a way to approximate differential operators on unstructured point clouds without the need for mesh generation. In this thesis, a 3d meshfree finite difference Poisson solver is presented. Its performance has been studies based on numerical convergence, parallel efficiency, and computational cost. Practical application of the solver is presented in a simulation of a potential flow field in a wall-bounded domain.</Abstract>
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