Fluid-structure interaction with applications in biomechanics

作     者：Hron, Jaroslav Madlik, Martin 

作者机构：Univ Dortmund Inst Appl Math D-44227 Dortmund Germany Charles Univ Prague Math Inst Prague 18675 Czech Republic 

出 版 物：《NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS》 (非线性分析：真实世界的应用)

年 卷 期：2007年第8卷第5期

页      面：1431-1458页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

主　　题：fluid-structure interaction monolithic ALE method biomechanics 

摘      要：In bioengineering applications problems of flow interacting with elastic solid are very common. We formulate the problem of interaction for an incompressible fluid and an incompressible elastic material in a fully coupled arbitrary Lagrangian-Eulerian (ALE) formulation. The mathematical description and the numerical schemes are designed in such a way that more complicated constitutive relations (and more realistic for bioengineering applications) can be incorporated easily. The whole domain of interest is treated as one continuum and the same discretization in space (FEM) and time (Crank-Nicholson) is used for both, solid and fluid, parts. The resulting nonlinear algebraic system is solved by an approximate Newton method. The combination of second order discretization and fully coupled solution method gives a method with high accuracy and robustness. To demonstrate the flexibility of this numerical approach we apply the same method to a mixture-based model of an elastic material with perfusion which also falls into the category of fluid structure interactions. A few simple example calculations with simple material models and large deformations of the solid part are presented. (c) 2006 Elsevier Ltd. All rights reserved.