Curvilinear Immersed Boundary Method for Simulating Fluid Structure Interaction with Complex 3D Rigid Bodies.
Curvilinear Immersed Boundary Method for Simulating Fluid Structure Interaction with Complex 3D Rigid Bodies.
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DOI：
10.1016/j.jcp.2008.04.028
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发表时间：
2008-08-10
影响因子：
4.1
通讯作者：
Sotiropoulos, Fotis
中科院分区：
文献类型：
--
作者：
Borazjani, Iman;Ge, Liang;Sotiropoulos, Fotis
将GE和Sotiropoulos的尖界面CURVIB方法[L.GE，F.Sotiropoulos，一种在具有复杂浸没边界的曲线区域中求解三维非定常不可压缩Navier-Stokes方程的数值方法]推广到计算物理杂志225(2007)1782-1809]，以模拟复杂三维刚体经历大结构位移的流体结构相互作用(FSI)问题。FSI解算器采用分区FSI求解方法，采用松耦合和强耦合两种策略。浸没物体和流体之间的界面用拉格朗日网格离散，并用显式前沿跟踪方法跟踪。为了快速识别背景网格和运动物体之间的关系，提出了一种高效的光线跟踪算法。对弹性安装圆柱体的涡激振动和生理条件下双叶机械心脏瓣膜的流动两个FSI问题进行了数值实验。对于这两种情况，计算结果与基准模拟和实验测量结果非常吻合。数值实验表明，结构的性质(质量、几何)和局部流动条件都对FSI算法的稳定性起着重要的作用。在一定条件下，即使采用强耦合FSI，迭代格式也是无条件不稳定的。然而，对于这种情况，强耦合迭代和欠松弛结合以及Aitken的加速技术被证明能有效地解决稳定性问题。给出了理论分析来解释数值实验的结果。结果表明，附加质量与结构质量的比值以及流体对结构施加的力或力矩的局部时间变化率的符号决定了FSI算法的稳定性和收敛速度。阐明了欠松弛的稳定作用，导出了稳定欠松弛系数的上界。
The sharp-interface CURVIB approach of Ge and Sotiropoulos [L. Ge, F. Sotiropoulos, A Numerical Method for Solving the 3D Unsteady Incompressible Navier-Stokes Equations in Curvilinear Domains with Complex Immersed Boundaries, Journal of Computational Physics 225 (2007) 1782–1809] is extended to simulate fluid structure interaction (FSI) problems involving complex 3D rigid bodies undergoing large structural displacements. The FSI solver adopts the partitioned FSI solution approach and both loose and strong coupling strategies are implemented. The interfaces between immersed bodies and the fluid are discretized with a Lagrangian grid and tracked with an explicit front-tracking approach. An efficient ray-tracing algorithm is developed to quickly identify the relationship between the background grid and the moving bodies. Numerical experiments are carried out for two FSI problems: vortex induced vibration of elastically mounted cylinders and flow through a bileaflet mechanical heart valve at physiologic conditions. For both cases the computed results are in excellent agreement with benchmark simulations and experimental measurements. The numerical experiments suggest that both the properties of the structure (mass, geometry) and the local flow conditions can play an important role in determining the stability of the FSI algorithm. Under certain conditions unconditionally unstable iteration schemes result even when strong coupling FSI is employed. For such cases, however, combining the strong-coupling iteration with under-relaxation in conjunction with the Aitken’s acceleration technique is shown to effectively resolve the stability problems. A theoretical analysis is presented to explain the findings of the numerical experiments. It is shown that the ratio of the added mass to the mass of the structure as well as the sign of the local time rate of change of the force or moment imparted on the structure by the fluid determine the stability and convergence of the FSI algorithm. The stabilizing role of under-relaxation is also clarified and an upper bound of the required for stability under-relaxation coefficient is derived.
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