Finite element computations for unsteady fluid and elastic membrane interaction problems
Finite element computations for unsteady fluid and elastic membrane interaction problems
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DOI：
10.1002/(sici)1097-0363(19970615)24:11
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发表时间：
1997-06
影响因子：
1.8
通讯作者：
S. Liang;G. Neitzel;C. Aidun
中科院分区：
文献类型：
--
作者：
S. Liang;G. Neitzel;C. Aidun
流场的流体动力和相邻可变形边界的弹性力之间的相互作用由弹性流体动力学（一种耦合的流体弹性膜问题）描述。非定常、高度非线性方程的直接数值解要求将流场和域形状的动态演化确定为解的一部分，因为两者都不是先验已知的。本文描述了一种基于变形空间域时空（DSD ST）有限元法的数值算法，用于不可压缩粘性流体与弹性膜相互作用的非定常运动。非定常Navier-斯托克方程和弹性膜方程分别使用迭代程序通过GMRES技术在每个时刻进行不完全的下-上（ILU）分解来求解。一维，二维和变形域模型的问题被用来证明本算法的能力和精度。稳态和瞬态问题进行了研究。出版社：John Wiley & Sons，Ltd.
SUMMARY The interaction between the hydrodynamic forces of a flow field and the elastic forces of adjacent deformable boundaries is described by elastohydrodynamics, a coupled fluid‐elastic membrane problem. Direct numerical solution of the unsteady, highly non-linear equations requires that the dynamic evolution of both the flow field and the domain shape be determined as part of the solution, since neither is known a priori. This paper describes a numerical algorithm based on the deformable spatial domain space‐time (DSD ST) finite element method for the unsteady motion of an incompressible, viscous fluid with elastic membrane interaction. The unsteady Navier‐ Stoke and elastic membrane equations are solved separately using an iterative procedure by the GMRES technique with an incomplete lower-upper (ILU) decomposition at every time instant. One-dimensional, twodimensional and deformable domain model problems are used to demonstrate the capabilities and accuracy of the present algorithm. Both steady state and transient problems are studied. 1997 by John Wiley & Sons, Ltd.