演化界面问题的非线性嵌入边界模型降阶
Reduction of Nonlinear Embedded Boundary Models for Problems with Evolving Interfaces
摘要：
嵌入式边界方法减轻了许多计算挑战，包括与网格化复杂几何形状和解决具有不断变化的域和界面的问题相关的挑战。然而，基于这种方法开发用于计算框架的模型降阶方法似乎具有挑战性。事实上，大多数流行的模型简化技术是基于投影的，并且依赖于从模拟快照的压缩中获得的基函数。在传统的界面拟合计算框架中，这种基函数的计算是直接的，主要是因为计算域在这种情况下不包含虚构的区域。然而，对于嵌入式计算框架，情况并非如此，因为在这种情况下，计算域通常包含真实区域和虚影区域，其定义使模拟快照的收集和压缩复杂化。当分隔两个区域的界面随时间演变时，问题会加剧。本文通过将快照压缩问题制定为加权低秩近似问题来解决这个问题，其中二进制加权识别各个模拟快照的演变组件。所提出的方法是独立于应用程序的，因此是全面的。它是成功地证明了几个二维的，涡主导的，流体-结构相互作用问题的模型减少。
英文摘要：
Embedded boundary methods alleviate many computational challenges, including those associated with meshing complex geometries and solving problems with evolving domains and interfaces. Developing model reduction methods for computational frameworks based on such methods seems however to be challenging. Indeed, most popular model reduction techniques are projection-based, and rely on basis functions obtained from the compression of simulation snapshots. In a traditional interface-fitted computational framework, the computation of such basis functions is straightforward, primarily because the computational domain does not contain in this case a fictitious region. This is not the case however for an embedded computational framework because the computational domain typically contains in this case both real and ghost regions whose definitions complicate the collection and compression of simulation snapshots. The problem is exacerbated when the interface separating both regions evolves in time. This paper addresses this issue by formulating the snapshot compression problem as a weighted low-rank approximation problem where the binary weighting identifies the evolving component of the individual simulation snapshots. The proposed approach is application independent and therefore comprehensive. It is successfully demonstrated for the model reduction of several two-dimensional, vortex-dominated, fluid-structure interaction problems.
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