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SAV decoupled ensemble algorithms for fast computation of Stokes–Darcy flow ensembles
Computer Methods in Applied Mechanics and Engineering ( IF 7.2 ) Pub Date : 2021-09-20 , DOI: 10.1016/j.cma.2021.114150
Nan Jiang 1 , Huanhuan Yang 2
Affiliation  

Numerical modeling and simulation of complex systems is often subject to uncertainties in model parameters. Many popular uncertainty quantification (UQ) methods require repeated simulations of the underlying physical system with different samples of the uncertain model parameters. This poses great challenges to many practical engineering applications due to the high demand for computational resources. In this report we propose highly efficient ensemble simulation algorithms for fast computation of coupled flow ensembles. The proposed ensemble algorithms are based on two recently developed numerical approaches: scalar auxiliary variable (SAV) and ensemble timestepping. We introduce a new decoupling strategy using the SAV idea and incorporate the ensemble timestepping method to develop two decoupled ensemble schemes for the Stokes–Darcy system: SAV-BE-En and SAV-BDF2-En. The two ensemble algorithms are specially designed for UQ computations where a number of realizations of the underlying coupled PDE system are required for analyzing and interpreting flow statistics. Compared with traditional methods which solve for each realization independently, our proposed ensemble algorithms result in a common coefficient matrix for all realizations and efficient iterative solvers such as block CG or block GMRES can be used to solve for all realizations simultaneously reducing both computer storage and overall simulation time. We prove that both ensemble algorithms are long time stable without any time step conditions. We also provide a comprehensive error analysis for the fully discrete SAV-BE-En algorithm, and present a few illustrative numerical examples to demonstrate the efficiency and effectiveness of the algorithms.



中文翻译:

用于快速计算斯托克斯-达西流系综​​的 SAV 解耦系综算法

复杂系统的数值建模和仿真常常受到模型参数的不确定性的影响。许多流行的不确定性量化 (UQ) 方法需要使用不确定模型参数的不同样本对底层物理系统进行重复模拟。由于对计算资源的高需求,这对许多实际工程应用提出了巨大挑战。在本报告中,我们提出了高效的集成用于快速计算耦合流系综的模拟算法。所提出的集成算法基于两种最近开发的数值方法:标量辅助变量 (SAV) 和集成时间步长。我们使用 SAV 思想引入了一种新的解耦策略,并结合集成时间步长方法为 Stokes-Darcy 系统开发了两种解耦集成方案:SAV-BE-En 和 SAV-BDF2-En。这两种集成算法专为 UQ 计算而设计,在这种情况下,分析和解释流统计需要底层耦合PDE 系统的许多实现。与独立求解每个实现的传统方法相比,我们提出的集成算法产生了一个公共系数矩阵对于所有实现,高效的迭代求解器(例如块 CG 或块 GMRES)可用于同时求解所有实现,从而减少计算机存储和整体仿真时间。我们证明了两种集成算法在没有任何时间步长条件的情况下都是长期稳定的。我们还对完全离散的 SAV-BE-En 算法进行了全面的误差分析,并提供了一些说明性的数值例子来证明算法的效率和有效性。

更新日期:2021-09-20
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