scholarly journals Nonconforming mixed finite element approximation of a fluid-structure interaction spectral problem

2016 ◽  
Vol 9 (1) ◽  
pp. 269-287
Author(s):  
Salim Meddahi ◽  
◽  
David Mora ◽  
Keyword(s):  
Finite Element ◽  
Spectral Problem ◽  
Mixed Finite Element ◽  
Fluid Structure Interaction ◽  
Finite Element Approximation ◽  
Element Approximation ◽  
Fluid Structure ◽  
Structure Interaction

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.

A mixed finite element method for the dynamic analysis of coupled fluid–solid interaction problems

1991 ◽  
Vol 433 (1888) ◽  
pp. 235-255 ◽  
Keyword(s):  
Finite Element ◽  
Variational Principle ◽  
Mixed Finite Element ◽  
Fluid Structure Interaction ◽  
Practical Interest ◽  
Elastic Solid ◽  
Matrix Equations ◽  
Dynamic Problems ◽  
Fluid Structure ◽  
Structure Interaction

On the basis of a variational principle, a mixed finite element approach is developed to describe the linear dynamics of coupled fluid–structure interactions. The variables of acceleration in the elastic solid and pressure in the fluid are adopted as the arguments of the variational principle. These are chosen since they directly relate to many practical fluid–structure interaction dynamic problems involving free surface disturbances, e. g. a dam-water system, a fuel cell in an aircraft, etc. Matrix equations describing the motions are presented and four methods of solution discussed, each simplifying and approximating the matrix equations for easier application to solve various types of engineering problems. This is demonstrated by analysing a selection of fluid–structure interaction problems of practical interest. The examples illustrate the general principle and application of the described functional approach without need to resort to more complex dynamic problems which can be analysed in a similar manner.

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