An immersogeometric variational framework for fluid-structure interaction: application to bioprosthetic heart valves.
An immersogeometric variational framework for fluid-structure interaction: application to bioprosthetic heart valves.
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DOI：
10.1016/j.cma.2014.10.040
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发表时间：
2015-02-01
影响因子：
7.2
通讯作者：
Hughes TJ
中科院分区：
文献类型：
--
作者：
Kamensky D;Hsu MC;Schillinger D;Evans JA;Aggarwal A;Bazilevs Y;Sacks MS;Hughes TJ
在本文中，我们开发了一个几何柔性技术的计算流固耦合（FSI）。激励应用是在整个心动周期内模拟三叶生物人工心脏瓣膜功能。由于心脏瓣膜小叶的复杂运动，流体域经历大的变形，包括拓扑结构的变化。所提出的方法直接分析了一个基于样条的表面表示的结构，通过将其浸入到一个非边界拟合的离散化周围的流体域。这将我们的方法在一个新兴的类的计算技术，旨在捕捉几何非边界拟合分析网格。我们引入术语“immersogeometric分析”来识别这种范式。该框架从一个增广拉格朗日制定FSI，强制执行运动学约束的组合拉格朗日乘数和惩罚力。对于浸没的体积对象，我们正式消除乘数场取代流体-结构界面的牵引力，到达Nitsche的方法，在物体表面上执行Dirichlet边界条件。对于浸入式薄壳结构，几何建模为表面，来自相对侧的牵引力由于背景流体解空间的连续性而抵消，留下罚方法。应用于生物人工心脏瓣膜，其中存在跨瓣叶的大的压力跳变，揭示了惩罚方法的缺点。为了抵消陡峭的压力梯度，通过结构没有条件的问题，伴随着强大的惩罚力，我们复活的拉格朗日乘子字段。此外，由于流体离散化不是针对结构几何形状的，因此在壳体上的压力不连续性的近似中存在显著误差。这种错误变得特别麻烦的残差为基础的稳定方法，不可压缩流，导致问题的压缩性在实际水平的细化。我们修改现有的稳定的方法，以提高性能。为了评估所提出的方法的准确性，我们测试他们的基准问题，并比较结果与已建立的边界拟合技术。最后，我们模拟了生理条件下的生物心脏瓣膜和周围血流的耦合，证明了所提出的技术在实际计算中的有效性。
In this paper, we develop a geometrically flexible technique for computational fluid–structure interaction (FSI). The motivating application is the simulation of tri-leaflet bioprosthetic heart valve function over the complete cardiac cycle. Due to the complex motion of the heart valve leaflets, the fluid domain undergoes large deformations, including changes of topology. The proposed method directly analyzes a spline-based surface representation of the structure by immersing it into a non-boundary-fitted discretization of the surrounding fluid domain. This places our method within an emerging class of computational techniques that aim to capture geometry on non-boundary-fitted analysis meshes. We introduce the term “immersogeometric analysis” to identify this paradigm. The framework starts with an augmented Lagrangian formulation for FSI that enforces kinematic constraints with a combination of Lagrange multipliers and penalty forces. For immersed volumetric objects, we formally eliminate the multiplier field by substituting a fluid–structure interface traction, arriving at Nitsche’s method for enforcing Dirichlet boundary conditions on object surfaces. For immersed thin shell structures modeled geometrically as surfaces, the tractions from opposite sides cancel due to the continuity of the background fluid solution space, leaving a penalty method. Application to a bioprosthetic heart valve, where there is a large pressure jump across the leaflets, reveals shortcomings of the penalty approach. To counteract steep pressure gradients through the structure without the conditioning problems that accompany strong penalty forces, we resurrect the Lagrange multiplier field. Further, since the fluid discretization is not tailored to the structure geometry, there is a significant error in the approximation of pressure discontinuities across the shell. This error becomes especially troublesome in residual-based stabilized methods for incompressible flow, leading to problematic compressibility at practical levels of refinement. We modify existing stabilized methods to improve performance. To evaluate the accuracy of the proposed methods, we test them on benchmark problems and compare the results with those of established boundary-fitted techniques. Finally, we simulate the coupling of the bioprosthetic heart valve and the surrounding blood flow under physiological conditions, demonstrating the effectiveness of the proposed techniques in practical computations.
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影响因子：
3.8
作者：
Aggarwal, Ankush;Ferrari, Giovanni;Joyce, Erin;Daniels, Michael J.;Sainger, Rachana;Gorman, Joseph H., III;Gorman, Robert;Sacks, Michael S.
通讯作者：
Sacks, Michael S.
DOI：
10.1016/j.cma.2008.11.020
发表时间：
2010-01-01
影响因子：
7.2
作者：
Bazilevs, Y.;Michler, C.;Hughes, T. J. R.
通讯作者：
Hughes, T. J. R.
DOI：
10.1016/0045-7825(91)90125-p
发表时间：
1991-01-01
影响因子：
7.2
作者：
BARBOSA, HJC;HUGHES, TJR
通讯作者：
HUGHES, TJR
影响因子：
2.1
作者：
Angot, P;Bruneau, CH;Fabrie, P
通讯作者：
Fabrie, P
影响因子：
4.1
作者：
Borazjani, Iman;Ge, Liang;Sotiropoulos, Fotis
通讯作者：
Sotiropoulos, Fotis