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.
- Fluids Engineering Division
Finite Element Approximation of the Extended Fluid-Structure Interaction (eXFSI) Problem
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Ebna Hai, BSM, Bause, M, & Kuberry, P. "Finite Element Approximation of the Extended Fluid-Structure Interaction (eXFSI) Problem." Proceedings of the ASME 2016 Fluids Engineering Division Summer Meeting collocated with the ASME 2016 Heat Transfer Summer Conference and the ASME 2016 14th International Conference on Nanochannels, Microchannels, and Minichannels. Volume 1A, Symposia: Turbomachinery Flow Simulation and Optimization; Applications in CFD; Bio-Inspired and Bio-Medical Fluid Mechanics; CFD Verification and Validation; Development and Applications of Immersed Boundary Methods; DNS, LES and Hybrid RANS/LES Methods; Fluid Machinery; Fluid-Structure Interaction and Flow-Induced Noise in Industrial Applications; Flow Applications in Aerospace; Active Fluid Dynamics and Flow Control — Theory, Experiments and Implementation. Washington, DC, USA. July 10–14, 2016. V01AT11A001. ASME. https://doi.org/10.1115/FEDSM2016-7506
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