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arXiv · 1705.09350

An efficient algorithm for simulating ensembles of parameterized flow problems

Max Gunzburger·Nan Jiang·Zhu Wang
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Abstract

Many applications of computational fluid dynamics require multiple simulations of a flow under different input conditions. In this paper, a numerical algorithm is developed to efficiently determine a set of such simulations in which the individually independent members of the set are subject to different viscosity coefficients, initial conditions, and/or body forces. The proposed scheme applied to the flow ensemble leads to need to solve a single linear system with multiple right-hand sides, and thus is computationally more efficient than solving for all the simulations separately. We show that the scheme is nonlinearly and long-term stable under certain conditions on the time-step size and a parameter deviation ratio. Rigorous numerical error estimate shows the scheme is of first-order accuracy in time and optimally accurate in space. Several numerical experiments are presented to illustrate the theoretical results.

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Max Gunzburger, Nan Jiang, Zhu Wang. 2017-05-25. An efficient algorithm for simulating ensembles of parameterized flow problems. https://arxiv.org/abs/1705.09350

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