scholarly journals Fully Eulerian finite element approximation of a fluid-structure interaction problem in cardiac cells

2013 ◽  
Vol 96 (11) ◽  
pp. 712-738 ◽  
Author(s):  
A. Laadhari ◽  
R. Ruiz-Baier ◽  
A. Quarteroni
Keyword(s):  
Finite Element ◽  
Fluid Structure Interaction ◽  
Finite Element Approximation ◽  
Cardiac Cells ◽  
Element Approximation ◽  
Fluid Structure ◽  
Structure Interaction ◽  
Interaction Problem

scholarly journals Finite Element Approximation of the Extended Fluid-Structure Interaction (eXFSI) Problem

2016 ◽  
Author(s):  
Bhuiyan Shameem Mahmood Ebna Hai ◽  
Markus Bause ◽  
Paul Kuberry
Keyword(s):  
Finite Element ◽  
Wave Propagation ◽  
Elastic Wave ◽  
Fluid Structure Interaction ◽  
Finite Element Approximation ◽  
Element Approximation ◽  
Fluid Structure ◽  
Strongly Coupled ◽  
Structure Interaction ◽  
Time Stepping

This contribution is the second part of three papers on Adaptive Multigrid Methods for the eXtended Fluid-Structure Interaction (eXFSI) Problem, where we introduce a monolithic variational formulation and solution techniques. To the best of our knowledge, such a model is new in the literature. This model is used to design an on-line structural health monitoring (SHM) system in order to determine the coupled acoustic and elastic wave propagation in moving domains and optimum locations for SHM sensors. In a monolithic nonlinear fluid-structure interaction (FSI), the fluid and structure models are formulated in different coordinate systems. This makes the FSI setup of a common variational description difficult and challenging. This article presents the state-of-the-art in the finite element approximation of FSI problem based on monolithic variational formulation in the well-established arbitrary Lagrangian Eulerian (ALE) framework. This research focuses on the newly developed mathematical model of a new FSI problem, which is referred to as extended Fluid-Structure Interaction (eXFSI) problem in the ALE framework. The eXFSI is a strongly coupled problem of typical FSI with a coupled wave propagation problem on the fluid-solid interface (WpFSI). The WpFSI is a strongly coupled problem of acoustic and elastic wave equations, where wave propagation problems automatically adopts the boundary conditions from the FSI problem at each time step. The ALE approach provides a simple but powerful procedure to couple solid deformations with fluid flows by a monolithic solution algorithm. In such a setting, the fluid problems are transformed to a fixed reference configuration by the ALE mapping. The goal of this work is the development of concepts for the efficient numerical solution of eXFSI problem, the analysis of various fluid-solid mesh motion techniques and comparison of different second-order time-stepping schemes. This work consists of the investigation of different time stepping scheme formulations for a nonlinear FSI problem coupling the acoustic/elastic wave propagation on the fluid-structure interface. Temporal discretization is based on finite differences and is formulated as a one step-θ scheme, from which we can consider the following particular cases: the implicit Euler, Crank-Nicolson, shifted Crank-Nicolson and the Fractional-Step-θ schemes. The nonlinear problem is solved with a Newton-like method where the discretization is done with a Galerkin finite element scheme. The implementation is accomplished via the software library package DOpElib based on the deal.II finite element library for the computation of different eXFSI configurations.

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