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dc.contributor.advisorLi, Xiaolinen_US
dc.contributor.authorKim, Joung-Dongen_US
dc.contributor.otherDepartment of Applied Mathematics and Statisticsen_US
dc.date.accessioned2013-05-24T16:38:21Z
dc.date.available2013-05-24T16:38:21Z
dc.date.issued1-May-12en_US
dc.date.submitted12-Mayen_US
dc.identifierStonyBrookUniversityETDPageEmbargo_20130517082608_116839en_US
dc.identifier.urihttp://hdl.handle.net/1951/60287
dc.description105 pg.en_US
dc.description.abstractWe use the front tracking method on a spring system to model the dynamic evolution of parachute canopies. The canopy surface of a parachute is represented by a triangulated surface mesh with preset equilibrium length on each side of the simplices. The stretching and wrinkling of the canopy and its supporting string chords (risers) are modeled by the spring system. The spring constants of the canopy and the risers are chosen based on the analysis of Young's modulus for fabric surface and string chord. The mass-spring system is a nonlinear ODE system. Added by the numerical and computational analysis, we show that the spring system has an upper bound of the eigen frequency. We analyzed the system by considering three spring models and we proved in one case that all eigenvalues are imaginary and there exists an upper bound for eigen-frequency. Based on this analysis, we analyzed the numerical accuracy and stability of the nonlinear spring mass system for fabric surface and its tangential and normal motion. We used the fourth order Runge-Kutta method to solve the ODE system and showed that the time step is linearly dependent on the mesh size for the system. And also high order method helps to control amplification of system. Damping is added to dissipate the excessive spring internal energy. The current model does not have radial reinforcement cables and has not taken into account the canopy porosity. This mechanical structure is coupled with the incompressible Navier-Stokes solver through the "Impulse method" which computes the velocity of the point mass by superposition of momentum. We analyzed the numerical stability of the spring system and used this computational module to simulate the flow pattern around a static parachute canopy and the dynamic evolution during the parachute inflation process. The numerical solutions have been compared with the available experimental data and there are good agreements in the terminal descent velocity and breathing frequency of the parachute.en_US
dc.description.sponsorshipStony Brook University Libraries. SBU Graduate School in Department of Applied Mathematics and Statistics. Charles Taber (Dean of Graduate School).en_US
dc.formatElectronic Resourceen_US
dc.language.isoen_USen_US
dc.publisherThe Graduate School, Stony Brook University: Stony Brook, NY.en_US
dc.subject.lcshApplied mathematicsen_US
dc.subject.othereigen frequency, front tracking, parachute inflation, spring modelen_US
dc.titleModeling of Parachute Dynamics with Front Tracking Methoden_US
dc.typeDissertationen_US
dc.description.advisorAdvisor(s): Li, Xiaolin . Committee Member(s): Glimm, James ; Jiao, Xiangmin ; Ladeinde, Foluso.en_US
dc.mimetypeApplication/PDFen_US


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