Accelerating and enabling convergence of nonlinear solvers for Navier–Stokes equations by continuous data assimilation
Accelerating and enabling convergence of nonlinear solvers for Navier–Stokes equations by continuous data assimilation
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通过连续数据同化加速并实现纳维斯托克斯方程非线性求解器的收敛
DOI：
10.1016/j.cma.2023.116313
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发表时间：
2023
影响因子：
7.2
通讯作者：
Vargun, Duygu
中科院分区：
文献类型：
--
作者：
Li, Xuejian;Hawkins, Elizabeth V.;Rebholz, Leo G.;Vargun, Duygu
本文考虑在有数据测量或解观测的情况下，改进N-S方程的Picard迭代求解器和牛顿迭代求解器。我们构造了自适应迭代，使用连续数据同化(CDA)风格的微推将已知的解数据合并到求解器中。对于CDA-Picard，我们证明了该方法比通常的Picard方法有更高的收敛速度，并且随着测量数据的增加，收敛速度也有所提高。我们还证明了CDA-Picard对于比通常的Picard更大的雷诺数是压缩的，并且包含的测量数据越多，在CDA-Picard仍然收缩的情况下，雷诺数就可以越大。对于CDA-牛顿模型，我们证明了对于初始猜想和雷诺数，收敛域随着测量数据量的增加而增大。此外，对于这两种方法，我们都展示了CDA可以作为将测量数据直接强制实施到解决方案中来实现。常见基准N-S试验的数值结果说明了这一理论。
This paper considers improving the Picard and Newton iterative solvers for the Navier–Stokes equations in the setting where data measurements or solution observations are available. We construct adapted iterations that use continuous data assimilation (CDA) style nudging to incorporate the known solution data into the solvers. For CDA-Picard, we prove the method has an improved convergence rate compared to usual Picard, and the rate improves as more measurement data is incorporated. We also prove that CDA-Picard is contractive for larger Reynolds numbers than usual Picard, and the more measurement data that is incorporated the larger the Reynolds number can be with CDA-Picard still being contractive. For CDA-Newton, we prove that the domain of convergence, with respect to both the initial guess and the Reynolds number, increases as the amount of measurement data is increased. Additionally, for both methods we show that CDA can be implemented as direct enforcement of measurement data into the solution. Numerical results for common benchmark Navier–Stokes tests illustrate the theory.
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DOI：
10.1017/9781108367639.006
发表时间：
2019-05
期刊：
Partial Differential Equations Arising from Physics and Geometry
影响因子：
--
作者：
A. Farhat;E. Lunasin;E. Titi
通讯作者：
A. Farhat;E. Lunasin;E. Titi
纳维-斯托克斯方程全离散混合有限元数据同化方案的误差分析
影响因子：
1.7
作者：
Bosco Garc'ia;J. Novo
通讯作者：
J. Novo
3D Ladyzhenskaya 模型的连续数据同化：分析和计算
DOI：
10.1016/j.nonrwa.2022.103659
发表时间：
2022
期刊：
Nonlinear Analysis: Real World Applications
影响因子：
--
作者：
Cao, Yu;Giorgini, Andrea;Jolly, Michael;Pakzad, Ali
通讯作者：
Pakzad, Ali
DOI：
10.1016/j.cma.2018.09.004
发表时间：
2018-05
影响因子：
7.2
作者：
Adam Larios;L. Rebholz;C. Zerfas
通讯作者：
Adam Larios;L. Rebholz;C. Zerfas
大数据下稳态纳维斯托克斯的独特性通过连续数据同化
影响因子：
1.3
作者：
Xuejian Li
通讯作者：
Xuejian Li