论文标题
降低订单剪切的有限元方法，用于几何参数化稳定和不稳定的Navier-Stokes问题
A Reduced Order Cut Finite Element method for geometrically parameterized steady and unsteady Navier-Stokes problems
论文作者
论文摘要
这项工作着重于稳定且不稳定的Navier-Stokes方程，以减少的订单建模框架。提出的方法基于一个级别的几何描述中适当的正交分解，并使用未固定的网格有限元法离散了感兴趣的问题。我们构建并研究了一个统一和几何独立的减少基础，这种基础克服了过去的许多障碍和并发症，这种障碍和并发症可能在发生几何形变时就会发生。通过使用独立的几何减少基础，我们能够避免重新构造和转换以参考配置，并且能够处理复杂的几何形状。在固定的扩展背景几何形状和降低的订单技术中，固定背景网格的这种组合在许多工业和工程应用中似乎有益且有利，过去无法有效解决。
This work focuses on steady and unsteady Navier-Stokes equations in a reduced order modeling framework. The methodology proposed is based on a Proper Orthogonal Decomposition within a levelset geometry description and the problems of interest are discretized with an unfitted mesh Finite Element Method. We construct and investigate a unified and geometry independent reduced basis which overcomes many barriers and complications of the past, that may occur whenever geometrical morphings are taking place. By employing a geometry independent reduced basis, we are able to avoid remeshing and transformation to reference configurations, and we are able to handle complex geometries. This combination of a fixed background mesh in a fixed extended background geometry with reduced order techniques appears beneficial and advantageous in many industrial and engineering applications, which could not be resolved efficiently in the past.
