The Natural Helmholtz-Hodge Decomposition for Open-Boundary Flow Analysis
The Natural Helmholtz-Hodge Decomposition for Open-Boundary Flow Analysis
复制标题
开放边界流分析的自然 Helmholtz-Hodge 分解
DOI：
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发表时间：
2014
影响因子：
5.2
通讯作者：
P. Bremer
中科院分区：
文献类型：
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作者：
H. Bhatia;Valerio Pascucci;P. Bremer
Helmholtz-Hodge分解(HHD)将流动描述为不可压缩流、无旋流和谐波流的总和，是模拟和分析的基本工具。遗憾的是，对于有界域，HHD并不是唯一定义的，传统上，边界条件是为了获得唯一解而施加的。但是，一般来说，模拟过程中使用的边界条件可能是未知的，或者模拟可能使用开放边界条件。在这些情况下，传统边界条件施加的流动可能与给定的数据不兼容，这导致有时在所有三个分量中都出现严重的伪影和扭曲，从而产生非物理结果。本文提出了自然HHD，通过将流动分为内部和外部两个部分来定义。使用完全数据驱动的方法，该方法无需假设先验的边界条件即可获得唯一性。因此，它能够对具有开放边界或未知边界条件的流动进行可靠且无伪影的分析。此外，与现有的全局技术不同，我们的方法是逐点计算HHD，从而支持计算任何域的子集的廉价的局部近似。最后，对于二维和三维的各种空间离散和插值场，该技术都很容易实现。
The Helmholtz-Hodge decomposition (HHD), which describes a flow as the sum of an incompressible, an irrotational, and a harmonic flow, is a fundamental tool for simulation and analysis. Unfortunately, for bounded domains, the HHD is not uniquely defined, traditionally, boundary conditions are imposed to obtain a unique solution. However, in general, the boundary conditions used during the simulation may not be known known, or the simulation may use open boundary conditions. In these cases, the flow imposed by traditional boundary conditions may not be compatible with the given data, which leads to sometimes drastic artifacts and distortions in all three components, hence producing unphysical results. This paper proposes the natural HHD, which is defined by separating the flow into internal and external components. Using a completely data-driven approach, the proposed technique obtains uniqueness without assuming boundary conditions a priori. As a result, it enables a reliable and artifact-free analysis for flows with open boundaries or unknown boundary conditions. Furthermore, our approach computes the HHD on a point-wise basis in contrast to the existing global techniques, and thus supports computing inexpensive local approximations for any subset of the domain. Finally, the technique is easy to implement for a variety of spatial discretizations and interpolated fields in both two and three dimensions.