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相关概念视频

Bernoulli's Equation for Flow Along a Streamline01:30

Bernoulli's Equation for Flow Along a Streamline

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Bernoulli's equation relates the energy conservation in a fluid moving along a streamline. The equation applies to incompressible and inviscid fluids under steady flow. For such a flow, Newton's second law is applied to a small fluid element, which experiences forces due to pressure differences, gravity, and velocity variations. The force balance leads to the following form of Bernoulli's equation:
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Turbulent Flow: Problem Solving01:09

Turbulent Flow: Problem Solving

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Carbonation is a process used to dissolve carbon dioxide gas in a liquid, commonly used in the production of carbonated beverages. Achieving efficient carbonation requires careful control of temperature, pressure, and flow conditions. By adjusting these parameters, carbonation efficiency can be maximized, producing a higher concentration of CO2 in the liquid.
Temperature is a key factor in CO2 solubility. In this case, the CO2 gas and the liquid are cooled to 20°C. Lower temperatures...
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Physiological Pharmacokinetic Models: Blood Flow-Limited Versus Diffusion-Limited Models00:57

Physiological Pharmacokinetic Models: Blood Flow-Limited Versus Diffusion-Limited Models

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Physiological pharmacokinetic models, often called flow-limited or perfusion models, typically assume a swift drug distribution between tissue and venous blood, creating a rapid drug equilibrium. This premise is based on the idea that drug diffusion is extremely fast, and the cell membrane presents no barrier to drug permeation. In this scenario, where no drug binding occurs, the drug concentration in the tissue equals that of the venous blood leaving the tissue. This greatly simplifies the...
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Control Volume and System Representations01:16

Control Volume and System Representations

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Two key frameworks are employed to analyze mass, energy, and momentum transfer: the control volume approach and the system approach. These frameworks offer different perspectives, depending on whether the focus is on a specific region in space (control volume approach) or a defined mass of fluid (system approach).
The control volume approach considers a stationary region in space through which fluid flows. This region is bounded by a control surface.  For instance, in the case of water...
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Bernoulli's Equation for Flow Normal to a Streamline01:16

Bernoulli's Equation for Flow Normal to a Streamline

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Bernoulli's equation for flow normal to a streamline explains how pressure varies across curved streamlines due to the outward centrifugal forces induced by the fluid's curvature. The pressure is higher on the inner side of the curve, near the center of curvature, and decreases outward to balance these centrifugal forces.
The pressure difference depends on the fluid's velocity and radius of curvature. The pressure variation is minimal in flows with nearly straight streamlines.
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Uniform Depth Channel Flow: Problem Solving01:18

Uniform Depth Channel Flow: Problem Solving

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To calculate the flow rate for a trapezoidal channel, first, identify the bottom width, side slope, and flow depth of the channel. The cross-sectional area (A) corresponding to the depth of flow (y), channel bottom width (B), and side slope (θ) is determined by:Next, calculate the wetted perimeter, which includes the bottom width and the sloped side lengths in contact with the water. Using the values of the cross-sectional area and the wetted perimeter, determine the hydraulic radius by...
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基于投影的减少顺序建模,用于3D心血管流动中不稳定的参数化最佳控制问题.

Surabhi Rathore1, Pasquale C Africa1, Francesco Ballarin2

  • 1mathLab, Mathematics Area, SISSA Scuola Internazionale Superiore di Studi Avanzati, Via Bonomea 265, Trieste, 34136, Italy.

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概括

本研究引入了基于投影的减少顺序建模 (ROM) 框架,通过控制外流边界条件来优化心血管 (CV) 血液动力学. 这种新的方法显著加快了患者特异性血管模型的模拟.

关键词:
心血管流动的心血管流动加勒金有限元素方法.拉格朗奇乘法器的使用方法嵌套适当的直角分解.最佳的控制控制是最好的控制.参数化的部分微分方程.

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科学领域:

  • 计算流体动力学 计算流体动力学
  • 生物医学工程 生物医学工程
  • 数学建模的数学建模

背景情况:

  • 准确的患者特异性心血管 (CV) 血液动力学建模受到复杂的血管几何形状和高计算成本的挑战.
  • 目前的方法很难整合临床数据,如4DMRI,以实现现实的流动模拟.
  • 优化外流边界条件对于可靠的CV血液动力学计算至关重要.

研究的目的:

  • 开发和介绍基于投影的减少顺序建模 (ROM) 框架,用于CV应用中的不稳定,参数化的最佳控制问题 (OCP).
  • 控制外流边界条件以优化心血管血液动力学和最大限度地减少流速配置中的差异.
  • 为了能够高效,准确地模拟患者特有的心血管流动.

主要方法:

  • 利用基于投影的减少技术与离线-在线的计算效率范式.
  • 采用Galerkin有限元法在线阶段计算高保真解决方案.
  • 实现了一个嵌套适当的直角分解 (嵌套-POD) 用于时间和参数空间压缩.

主要成果:

  • 在理想化和患者特定的血管模型 (冠状动脉旁路移植) 上证明了框架的有效性.
  • 与高保真模拟策略相比,实现了一致的加快速度.
  • 提供了对流动特征和影响动脉样硬化风险的因素的见解.

结论:

  • 基于投影的ROM框架为模拟参数化的CV流提供了一种高效准确的方法.
  • 实现实时,针对患者的具体建模,以实现个性化医疗干预.
  • 改善血管区域疾病进展的预测.