A finite element method for the Navier-Stokes equations in moving domain with application to hemodynamics of the left ventricle
A finite element method for the Navier-Stokes equations in moving domain with application to hemodynamics of the left ventricle
复制标题
运动域纳维-斯托克斯方程的有限元方法及其在左心室血流动力学中的应用
DOI：
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
Y. Vassilevski
中科院分区：
文献类型：
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作者：
A. Danilov;A. Lozovskiy;M. Olshanskii;Y. Vassilevski
本文介绍了一种求解不可压缩粘性流体时变域N-S方程的有限元方法。该方法基于问题的拟拉格朗日形式，并以时间显式的方式处理几何问题。我们证明了数值解满足基本能量估计的离散模拟。这种稳定性估计不需要CFL时间步长限制。该方法被进一步应用于人体心脏左心室模型中的流动的模拟，其中室壁动力学是从一系列对比增强的计算机断层扫描图像重建的。
Abstract The paper introduces a finite element method for the Navier-Stokes equations of incompressible viscous fluid in a time-dependent domain. The method is based on a quasi-Lagrangian formulation of the problem and handling the geometry in a time-explicit way. We prove that numerical solution satisfies a discrete analogue of the fundamental energy estimate. This stability estimate does not require a CFL time-step restriction. The method is further applied to simulation of a flow in a model of the left ventricle of a human heart, where the ventricle wall dynamics is reconstructed from a sequence of contrast enhanced Computed Tomography images.