Hybrid finite difference/finite element immersed boundary method

被引:98
作者
Griffith, Boyce E. [1 ,2 ,3 ]
Luo, Xiaoyu [4 ]
机构
[1] Univ N Carolina, Dept Math, Chapel Hill, NC USA
[2] Univ N Carolina, Dept Biomed Engn, Carolina Ctr Interdisciplinary Appl Math, Chapel Hill, NC USA
[3] Univ N Carolina, McAllister Heart Inst, Chapel Hill, NC USA
[4] Univ Glasgow, Sch Math & Stat, Glasgow, Lanark, Scotland
基金
美国国家卫生研究院; 美国国家科学基金会; 英国工程与自然科学研究理事会;
关键词
finite difference method; finite element method; fluid-structure interaction; immersed boundary method; incompressible elasticity; incompressible flow; FLUID-STRUCTURE INTERACTION; HEART DIASTOLIC FUNCTION; NAVIER-STOKES EQUATIONS; INTERFACE METHOD; LEFT-VENTRICLE; COMPUTATIONAL MODEL; BLOOD-FLOW; DYNAMICS; ACCURATE; IMPLEMENTATION;
D O I
10.1002/cnm.2888
中图分类号
R318 [生物医学工程];
学科分类号
0831 ;
摘要
The immersed boundary method is an approach to fluid-structure interaction that uses a Lagrangian description of the structural deformations, stresses, and forces along with an Eulerian description of the momentum, viscosity, and incompressibility of the fluid-structure system. The original immersed boundary methods described immersed elastic structures using systems of flexible fibers, and even now, most immersed boundary methods still require Lagrangian meshes that are finer than the Eulerian grid. This work introduces a coupling scheme for the immersed boundary method to link the Lagrangian and Eulerian variables that facilitates independent spatial discretizations for the structure and background grid. This approach uses a finite element discretization of the structure while retaining a finite difference scheme for the Eulerian variables. We apply this method to benchmark problems involving elastic, rigid, and actively contracting structures, including an idealized model of the left ventricle of the heart. Our tests include cases in which, for a fixed Eulerian grid spacing, coarser Lagrangian structural meshes yield discretization errors that are as much as several orders of magnitude smaller than errors obtained using finer structural meshes. The Lagrangian-Eulerian coupling approach developed in this work enables the effective use of these coarse structural meshes with the immersed boundary method. This work also contrasts two different weak forms of the equations, one of which is demonstrated to be more effective for the coarse structural discretizations facilitated by our coupling approach.
引用
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页数:31
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