Explicit treatment for Dirichlet, Neumann and Cauchy boundary conditions in POD-based reduction of groundwater models
Explicit treatment for Dirichlet, Neumann and Cauchy boundary conditions in POD-based reduction of groundwater models
复制标题
基于 POD 的地下水还原模型中 Dirichlet、Neumann 和 Cauchy 边界条件的显式处理
DOI：
10.1016/j.advwatres.2018.03.011
复制
发表时间：
2018
影响因子：
4.7
通讯作者：
Wöhling
中科院分区：
文献类型：
--
作者：
Gosses;Wöhling
本征正交分解（POD）是近年来地下水建模领域中一种流行的模型降阶方法。它用于缓解通常与基于物理的自然系统建模相关的长运行时间问题，特别是用于参数估计和不确定性分析。POD为基础的技术再现地下水水头场足够准确的各种应用。然而，没有研究调查POD技术如何影响地下水模型中发现的不同边界条件的准确性。我们发现，目前的POD边界条件的处理导致这些边界的简化模型中的不准确。我们提供了一种改进的方法，该方法将POD投影空间分成与边界条件正交的子空间和强制执行边界条件的单独子空间。为了测试Dirichlet，Neumann和Cauchy边界条件的方法，四个简单的瞬态一维地下水模型，以及一个更复杂的三维模型，建立和减少标准POD和POD与新的扩展。我们表明，在对比标准POD，新的方法同时满足狄利克雷和诺依曼边界条件。它也可以应用到柯西边界，其中标准POD的通量误差通过其头独立贡献而减小。这种延伸实质上是将投影的焦点移向边界条件。因此，我们看到模型边界处的误差与简化模型的总体精度之间存在轻微的权衡。在需要精确处理边界条件的情况下，建议使用POD扩展。
In recent years, proper orthogonal decomposition (POD) has become a popular model reduction method in the field of groundwater modeling. It is used to mitigate the problem of long run times that are often associated with physically-based modeling of natural systems, especially for parameter estimation and uncertainty analysis. POD-based techniques reproduce groundwater head fields sufficiently accurate for a variety of applications. However, no study has investigated how POD techniques affect the accuracy of different boundary conditions found in groundwater models. We show that the current treatment of boundary conditions in POD causes inaccuracies for these boundaries in the reduced models. We provide an improved method that splits the POD projection space into a subspace orthogonal to the boundary conditions and a separate subspace that enforces the boundary conditions. To test the method for Dirichlet, Neumann and Cauchy boundary conditions, four simple transient 1D-groundwater models, as well as a more complex 3D model, are set up and reduced both by standard POD and POD with the new extension. We show that, in contrast to standard POD, the new method satisfies both Dirichlet and Neumann boundary conditions. It can also be applied to Cauchy boundaries, where the flux error of standard POD is reduced by its head-independent contribution. The extension essentially shifts the focus of the projection towards the boundary conditions. Therefore, we see a slight trade-off between errors at model boundaries and overall accuracy of the reduced model. The proposed POD extension is recommended where exact treatment of boundary conditions is required.
登录
查看更多内容
影响因子：
5.4
作者：
Doherty, John;Christensen, Steen
通讯作者：
Christensen, Steen
DOI：
--
发表时间：
2006
期刊：
影响因子：
--
作者：
G. Pinder;M. Celia
通讯作者：
M. Celia
影响因子：
4.7
作者：
Boyce, Scott E.;Nishikawa, Tracy;Yeh, William W-G.
通讯作者：
Yeh, William W-G.
非线性问题降阶模型中基本边界条件的一般处理
影响因子：
--
作者：
Alejandro Cosimo;A. Cardona;S. Idelsohn
通讯作者：
S. Idelsohn
影响因子：
5.4
作者：
Fienen, Michael N.;Masterson, John P.;Thieler, E. Robert
通讯作者：
Thieler, E. Robert