Algorithms for fluid-structure interaction problems arising in hemodynamics
Algorithms for fluid-structure interaction problems arising in hemodynamics
复制标题
血流动力学中出现的流固耦合问题的算法
DOI：
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
A. Quaini
中科院分区：
文献类型：
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作者：
A. Quaini
在这篇论文中，我们讨论了流体-结构相互作用（FSI）问题的数值近似，并特别关注（尽管不是唯一的）血流动力学应用。首先，我们将血液建模为不可压缩的流体，将动脉壁建模为弹性结构。为了解决耦合问题，我们提出了一种新的半隐式算法，该算法基于FSI问题的时空离散化和线性化后得到的线性系统的不精确块lu分解。因此，每次迭代时流体速度与耦合压力-结构速度系统分开计算，从而降低了计算成本。这种方法导致了两种不同的方法家族，它们扩展到以前用于纯流体问题的FSI问题方案。对基于两种预条件的非精确分解算法与其他FSI系统的算法进行了比较。第一个是经典的Dirichlet-Neumann预条件，它具有模块化的优点（即它允许以最小的努力重用现有的流体和结构代码）。不幸的是，它的性能非常差的情况下，大的附加质量效应，因为它发生在血流动力学。或者，我们考虑一种非模块化的方法，它包括用合适的对角缩放结合ILUT预调节器对耦合系统进行预处理。然后用克里洛夫法求解该系统。这个过程的缺点是失去了模块化。在独立于预条件的情况下，突出了半隐式算法的效率。所有的方法都在二维和三维血管系统上进行了测试。将非模块化ILUT预调节器与Krylov方法相结合的算法是最快的。然而，不应该忽视基于模块化和非精确分解的方法，因为它们可以从代码并行化中获益，这与ILUT-Krylov方法不同。最后，我们改进了结构模型，将血管壁表示为线性孔隙弹性介质。我们的非模方法和从区域分解角度产生的分割过程扩展到流体-孔隙弹性结构相互作用。在简化的血管系统中，对它们的数值性能进行了分析和比较。
We discuss in this thesis the numerical approximation of fluid-structure interaction (FSI) problems with a particular concern (albeit not exclusive) on hemodynamics applications. Firstly, we model the blood as an incompressible fluid and the artery wall as an elastic structure. To solve the coupled problem, we propose new semi-implicit algorithms based on inexact block-LU factorization of the linear system obtained after the space-time discretization and linearization of the FSI problem. As a result, the fluid velocity is computed separately from the coupled pressure-structure velocity system at each iteration, hence reducing the computational cost. This approach leads to two different families of methods which extend to FSI problems schemes that were previously adopted for pure fluid problems. The algorithms derived from inexact factorization methods are compared with other schemes based on two preconditioners for the FSI system. The first one is the classical Dirichlet-Neumann preconditioner, which has the advantage of modularity (i.e. it allows to reuse existing fluid and structure codes with minimum effort). Unfortunately, its performance is very poor in case of large added-mass effect, as it happens in hemodynamics. Alternatively, we consider a non-modular approach which consists in preconditioning the coupled system with a suitable diagonal scaling combined with an ILUT preconditioner. The system is then solved by a Krylov method. The drawback of this procedure is the loss of modularity. Independently of the preconditioner, the efficiency of semi-implicit algorithms is highlighted. All the methods are tested on two and three-dimensional blood-vessel systems. The algorithm combining the non-modular ILUT preconditioner with Krylov methods proved to be the fastest. However, modular and inexact factorization based methods should not be disregarded because they can considerably benefit from code parallelization, unlike the ILUT-Krylov approach. Finally, we improve the structure model by representing the vessel wall as a linear poroelastic medium. Our non-modular approach and the partitioned procedures arising from a domain decomposition viewpoint are extended to fluid-poroelastic structure interactions. Their numerical performance are analyzed and compared on simplified blood-vessel systems.
老化和压力对主动脉壁特定水力传导率的影响。
影响因子：
1.1
作者：
Whale,MD;Grodzinsky,AJ;Johnson,M
通讯作者：
Johnson,M