计算降维策略用于不可压缩流体动力学中稳态分支点检测：应用于心脏科的Coanda效应
Computational reduction strategies for the detection of steady bifurcations in incompressible fluid-dynamics: applications to Coanda effect in cardiology
AI总结：
本文提出利用降维建模技术降低检测流体动力学稳态分支点的计算成本，应用于血流中二尖瓣反流时对称性破缺的分析。
摘要：
我们关注减少不可压缩纳维-斯托克斯方程解的流体稳定性计算成本，特别是在收缩-扩张通道中牛顿粘性流体的情况。特别关注当物理或几何控制参数变化时出现的稳态分支点，此时非唯一稳定解出现。稳定性问题的提出需要求解偏微分算子的特征值问题。另一种方法是直接模拟流体以表征解的渐近行为。这两种方法在计算时间上都非常昂贵。我们提出应用降维建模（ROM）技术来降低检测流体动力学中一种稳态分支点的计算成本。促使本研究的应用是血流通过反流二尖瓣时，根据雷诺数和反流二尖瓣孔形状出现的不对称性（即对称性破缺分支点）。
英文摘要：
We focus on reducing the computational costs associated with the hydrodynamic stability of solutions of the incompressible Navier-Stokes equations for a Newtonian and viscous fluid in contraction-expansion channels. In particular, we are interested in studying steady bifurcations, occurring when non-unique stable solutions appear as physical and/or geometric control parameters are varied. The formulation of the stability problem requires solving an eigenvalue problem for a partial differential operator. An alternative to this approach is the direct simulation of the flow to characterize the asymptotic behavior of the solution. Both approaches can be extremely expensive in terms of computational time. We propose to apply Reduced Order Modeling (ROM) techniques to reduce the demanding computational costs associated with the detection of a type of steady bifurcations in fluid dynamics. The application that motivated the present study is the onset of asymmetries (i.e., symmetry breaking bifurcation) in blood flow through a regurgitant mitral valve, depending on the Reynolds number and the regurgitant mitral valve orifice shape.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
