科研之友
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摘要
The propagation of uncertainty in physical parameters of fluid-structure interaction problems is a challenging task-both mathematically and in terms of computational workload. In this paper, we employ nonintrusive polynomial chaos expansion and model the uncertainty in five independent input parameters that characterize both fluid and structure. We propose a novel methodology to compute the expansion's coefficients using spatially adaptive sparse grids and products of one-dimensional integrals, which exploits the tensor structure of both sparse grids and probabilistic space. Furthermore, with spatial adaptivity and modified basis functions, we keep the number of sparse grid points small. We test our approach in two test cases: (i) an elastic vertical flap in a channel flow and (ii) a computationally challenging, well-established benchmark. The outputs of interest are the x-deflection and total force on the structure. In the first test case, we consider six implementations of our methodology and two established methods based on sparse grid quadrature. We evaluate the performance (in terms of number of runs of the numerical solver) and accuracy of all eight methods. The results show that one variant of our approach outperforms all the other implementations. We apply our best variant to the benchmark scenario and address the high computational demands of the resulting problem using three levels of parallelism. Importantly, our approach is not restricted to fluid-structure interaction problems. We can address a broad spectrum of computationally expensive problems, provided that sparse grid approximations can be employed.
- 出版日期2018
