Modeling of Parachute Dynamics with GPU Enhanced Continuum Fabric Model and Front Tracking Method

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 6x 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 7-20x 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 2x speedup for pricing single option and 400x speedup for multiple options.