An efficient algorithm for simulating ensembles of parameterized flow problems
An efficient algorithm for simulating ensembles of parameterized flow problems
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DOI：
10.1093/imanum/dry029
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发表时间：
2017-05
期刊：
影响因子：
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通讯作者：
M. Gunzburger;N. Jiang;Zhu Wang
中科院分区：
文献类型：
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作者：
M. Gunzburger;N. Jiang;Zhu Wang
计算流体力学的许多应用需要对不同输入条件下的流动进行多次模拟。本文开发了一种数值算法来有效地确定这样一组模拟，在该组模拟中，独立的成员受到不同的粘性系数、初始条件和/或体力。将该方法应用于流系综时，需要求解一个具有多个右端的线性方程组，因此比单独求解所有模拟的计算效率更高。我们证明了该格式在一定的时间步长和参数偏差率下是非线性的和长期稳定的。严格的数值误差估计表明，该格式在时间上具有一阶精度，在空间上具有最优精度。文中给出了几个数值实验来验证理论结果。
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.