An Operator Splitting Approach to the Solution of Fluid-Structure Interaction Problems in Hemodynamics
An Operator Splitting Approach to the Solution of Fluid-Structure Interaction Problems in Hemodynamics
复制标题
求解血液动力学流固耦合问题的算子分裂法
DOI：
10.1007/978-3-319-41589-5_22
复制
发表时间：
2016
影响因子：
2.4
通讯作者：
R. Glowinski
中科院分区：
文献类型：
--
作者：
M. Bukač;S. Čanić;B. Muha;R. Glowinski
我们提出了一种松耦合分区方法，用于血液动力学中一类流固相互作用问题的数值模拟。该方法基于李类型的算子分割方案的时间离散化。假设结构很薄，并通过 Koiter 壳或膜方程进行建模，而流体则通过不可压缩粘性流体的 3D 纳维-斯托克斯方程进行建模。流体和结构通过在移动的流体-结构界面处发生的完全双向耦合来耦合，从而产生非线性移动边界问题。李分裂将流体和结构子问题解耦，其设计方式使得所得分区方案无条件稳定，无需在每个时间步进行任何子迭代。使用能量估计讨论了该方案的无条件稳定性，并给出了几个数值例子，表明该方案在时间上是一阶精确的。实现简单、计算效率高、模块化和无条件稳定性使得该方案对于解决血流动力学中的 FSI 特别有吸引力。
We present a loosely coupled partitioned method for the numerical simulation of a class of fluid-structure interaction problems in hemodynamics. This method is based on a time discretization by an operator-splitting scheme of the Lie’s type. The structure is assumed to be thin and modeled by the Koiter shell or membrane equations, while the fluid is modeled by the 3D Navier-Stokes equations for an incompressible viscous fluid. The fluid and structure are coupled via a full two-way coupling taking place at the moving fluid-structure interface, thus giving rise to a nonlinear moving-boundary problem. The Lie splitting decouples the fluid and structure sub-problems and is designed in such a way that the resulting partitioned scheme is unconditionally stable, without the need for any sub-iterations at every time step. Unconditional stability of the scheme is discussed using energy estimates, and several numerical examples are presented, showing that the scheme is first-order accurate in time. Implementation simplicity, computational efficiency, modularity, and unconditional stability make this scheme particularly appealing for solving FSI in hemodynamics.