A quasi-Lagrangian finite element method for the Navier-Stokes equations in a time-dependent domain
A quasi-Lagrangian finite element method for the Navier-Stokes equations in a time-dependent domain
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DOI：
10.1016/j.cma.2018.01.024
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发表时间：
2017-07
影响因子：
7.2
通讯作者：
A. Lozovskiy;M. Olshanskii;Y. Vassilevski
中科院分区：
文献类型：
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作者：
A. Lozovskiy;M. Olshanskii;Y. Vassilevski
本文建立了不可压缩黏性流体的Navier-Stokes方程的时域有限元解法。该方法建立在问题的准拉格朗日公式的基础上。本文给出了全离散（时间有限差分和空间有限元）方法的稳定性和收敛性分析。本分析不假设任何CFL时间步长限制，只需要Δ t≤C形式的温和条件，其中C仅取决于问题数据，h 2 m u+ 2≤C Δ t， m u为多项式速度度有限元空间。这两个条件都是对实际重要的非齐次边界条件进行数值处理的结果。通过一组数值实验验证了理论预测的收敛率。此外，我们将该方法应用于模拟人类心脏左心室的简化模型中的流动，其中心室壁动力学是从一系列对比度增强的计算机断层扫描图像中重建的。
The paper develops a finite element method for the Navier–Stokes equations of incompressible viscous fluid in a time-dependent domain. The method builds on a quasi-Lagrangian formulation of the problem. The paper provides stability and convergence analysis of the fully discrete (finite-difference in time and finite-element in space) method. The analysis does not assume any CFL time-step restriction, it rather needs mild conditions of the form Δ t≤ C, where C depends only on problem data, and h 2 m u+ 2≤ c Δ t, m u is polynomial degree of velocity finite element space. Both conditions result from a numerical treatment of practically important non-homogeneous boundary conditions. The theoretically predicted convergence rate is confirmed by a set of numerical experiments. Further we apply the method to simulate a flow in a simplified 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.