Type
Text
Type
Dissertation
Advisor
Glimm, James | Li, Xiaolin | Jiao, Xiangmin | Ladeinde, Foluso.
Date
2014-12-01
Keywords
elastic membrane, front tracking, parachute inflation, spring model | Aerospace engineering
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/11401/76327
Publisher
The Graduate School, Stony Brook University: Stony Brook, NY.
Format
application/pdf
Abstract
An advanced mesoscale spring-mass model is used to mimic fabric surface motion. The fabric surface is represented by a high-quality triangular surface mesh. Both the tensile stiffness and the angular stiffness of each spring are determined by the material's Young's modulus and Poisson ratio, as well as the geometrical characteristics of the surface mesh. The spring-mass system is a nonlinear Ordinary Differential Equation (ODE) system solved by fourth order Runge-Kutta method. The model is shown to be numerically convergent under the constraint that the summation of points masses is constant. Through coupling with an incompressible fluid solver and the front tracking method, the spring-mass model is applied to the simulation of the dynamic phenomenon of parachute inflation. Complex validation simulations conclude the effort via drag force comparisons with experiments. Three applications of Graphics Processing Unit (GPU)-based algorithms for high performance computation of mathematical models were reported. Using one GPU device in the solving of the spring-mass system, we have achieved 6× speedup. In the second set of simulations, the system of one-dimensional gas dynamics equations is solved by the Weighted Essentially Non-Oscillatory (WENO) scheme; the GPU code is 7-20× faster than the pure CPU code. In the last case, a GPU enhanced numerical algorithm for American option pricing under the generalized hyperbolic distribution is studied. We have achieved 2× speedup for pricing single option and 400× speedup for multiple options. | An advanced mesoscale spring-mass model is used to mimic fabric surface motion. The fabric surface is represented by a high-quality triangular surface mesh. Both the tensile stiffness and the angular stiffness of each spring are determined by the material's Young's modulus and Poisson ratio, as well as the geometrical characteristics of the surface mesh. The spring-mass system is a nonlinear Ordinary Differential Equation (ODE) system solved by fourth order Runge-Kutta method. The model is shown to be numerically convergent under the constraint that the summation of points masses is constant. Through coupling with an incompressible fluid solver and the front tracking method, the spring-mass model is applied to the simulation of the dynamic phenomenon of parachute inflation. Complex validation simulations conclude the effort via drag force comparisons with experiments. Three applications of Graphics Processing Unit (GPU)-based algorithms for high performance computation of mathematical models were reported. Using one GPU device in the solving of the spring-mass system, we have achieved 6× speedup. In the second set of simulations, the system of one-dimensional gas dynamics equations is solved by the Weighted Essentially Non-Oscillatory (WENO) scheme; the GPU code is 7-20× faster than the pure CPU code. In the last case, a GPU enhanced numerical algorithm for American option pricing under the generalized hyperbolic distribution is studied. We have achieved 2× speedup for pricing single option and 400× speedup for multiple options. | 130 pages
Recommended Citation
Shi, Qiangqiang, "Modeling of Parachute Dynamics with GPU Enhanced Continuum Fabric Model and Front Tracking Method" (2014). Stony Brook Theses and Dissertations Collection, 2006-2020 (closed to submissions). 2251.
https://commons.library.stonybrook.edu/stony-brook-theses-and-dissertations-collection/2251