COLLABORATIVE PROPOSAL: Enhanced Least-Squares Methods for PIV Analysis

协作提案：用于 PIV 分析的增强型最小二乘法

• 批准号: 0810891
• 负责人: Jeffrey Heys
• 金额: $ 12.21万
• 依托单位: Montana State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2008
• 资助国家: 美国
• 起止时间: 2008-09-15 至 2012-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0810891&HistoricalAwards=false
• 关键词: COLLABORATIVE; PROPOSAL; Enhanced; Least; Squares

Particle Image Velocimetry (PIV) is a method for obtaining a fluid velocity field based on the translation of particles between images with a known time span between them. A potential limitation of PIV is that only two-dimensional velocity field along a single plane can be obtained from a two-dimensional image. This limitation is normally overcome by designing the experimental flow system so that the third velocity component is either zero or unimportant. In many applications, however, it is not possible to simplify the fully three-dimensional velocity field (e.g., in the left ventricle of the heart), and the two-dimensional limitations associated with PIV analysis are a significant problem that must be overcome. Would it be possible, however, to combine the two-dimensional PIV data together with a fully three-dimensional numerical approximation to the Navier-Stokes equations and obtain a sufficiently accurate three-dimensional velocity field in a domain such as the left ventricle of the heart? The use of least-squares finite element methods (LSFEMs) is proposed here to approximately solve the Navier-Stokes equations, and, significantly, to weakly constrain the solution along the PIV plane to match the experimental data. The PIV data would basically act as an internal boundary, and the numerical solution would weakly match the data with a variable weighting that determines the strength of the coupling between the data and numerical solution. LSFEMs are uniquely well suited for solving an over-constrained problem like this in a computationally efficient manner.Echocardiologists have developed methods for introducing microbubbles into circulating blood that can be resolved using ultrasound. The location of the microbubbles combined with the high temporal resolution of ultrasound allows the local blood velocity to be determined using Particle Image Velocimetry, but the high temporal resolution requirement also limits the ultrasound scans (and, hence, the velocity field data) to two dimensions. One goal of using the FDA approved microbubbles is to use the blood velocity data to calculate physiologically important information such as pressure gradients and energy loss for the blood flow, but these calculations require a full three-dimensional velocity field. The goal of the proposed research is to develop mathematical techniques that combine computational fluid dynamics with experimental velocity data, such as that from microbubbles, to obtain a full, three-dimensional velocity field, thus providing greater insight into the dynamics of the flow.

粒子图像测速（PIV）是一种基于已知时间跨度的图像之间的粒子平移来获得流体速度场的方法。PIV的一个潜在限制是，从二维图像中只能获得沿单个平面的二维速度场。通过设计实验流系统，使第三速度分量为零或不重要，通常可以克服这一限制。然而，在许多应用中，不可能简化完全三维的速度场（例如，在心脏的左心室），并且与PIV分析相关的二维限制是必须克服的重要问题。然而，是否有可能将二维PIV数据与Navier-Stokes方程的全三维数值近似结合起来，在心脏左心室等区域获得足够精确的三维速度场？本文提出了利用最小二乘有限元法（lsfem）近似求解Navier-Stokes方程，并在PIV平面上对解进行弱约束以匹配实验数据。PIV数据基本上充当内部边界，数值解将用变量权重弱匹配数据，变量权重决定数据和数值解之间的耦合强度。lsfem非常适合以高效的计算方式解决此类过度约束问题。超声心脏病专家已经开发出了将微气泡引入循环血液的方法，这些方法可以用超声波来解决。微泡的位置与超声的高时间分辨率相结合，允许使用粒子图像测速法确定局部血液速度，但高时间分辨率要求也限制了超声扫描（因此，速度场数据）为二维。使用FDA批准的微气泡的一个目标是使用血液流速数据来计算生理上重要的信息，如血液流动的压力梯度和能量损失，但这些计算需要一个完整的三维速度场。提出的研究目标是发展数学技术，将计算流体动力学与实验速度数据（如来自微泡的数据）相结合，以获得完整的三维速度场，从而更深入地了解流动动力学。