Adaptive Finite Elements Simulation Methods and Applications for Monolithic Fluid-Structure Interaction (FSI) Problem

2014 ◽  
Author(s):  
Bhuiyan Shameem Mahmood Ebna Hai ◽  
Markus Bause
Keyword(s):  
Fluid Dynamics ◽  
Structural Analysis ◽  
Solid Mechanics ◽  
Stokes Equations ◽  
Fluid Structure Interaction ◽  
Finite Difference Schemes ◽  
Fluid Structure ◽  
Structure Interaction ◽  
Time Stepping ◽  
Crank Nicolson

Will an aircraft wing have the structural integrity to withstand the forces or fail when it’s racing at a full speed? Fluid-structure interaction (FSI) analysis can help you to answer this question without the need to create costly prototypes. However, combining fluid dynamics with structural analysis traditionally poses a formidable challenge for even the most advanced numerical techniques due to the disconnected, domain-specific nature of analysis tools. In this paper, we present the state-of-the-art in computational FSI methods and techniques that go beyond the fundamentals of computational fluid and solid mechanics. In fact, the fundamental rule require transferring results from the computational fluid dynamics (CFD) analysis as input into the structural analysis and thus can be time-consuming, tedious and error-prone. This work consists of the investigation of different time stepping scheme formulations for a nonlinear fluid-structure interaction problem coupling the incompressible Navier-Stokes equations with a hyperelastic solid based on the well established Arbitrary Lagrangian Eulerian (ALE) framework. Temporal discretization is based on finite differences and a formulation as one step-θ scheme, from which we can extract the implicit euler, crank-nicolson, shifted crank-nicolson and the fractional-step-θ schemes. The ALE approach provides a simple, but powerful procedure to couple fluid flows with solid deformations by a monolithic solution algorithm. In such a setting, the fluid equations are transformed to a fixed reference configuration via the ALE mapping. The goal of this work is the development of concepts for the efficient numerical solution of FSI problem and the analysis of various fluid-mesh motion techniques, a comparison of different second-order time-stepping schemes. The time discretization is based on finite difference schemes whereas the spatial discretization is done with a Galerkin finite element scheme. The nonlinear problem is solved with Newton’s method. To control computational costs, we apply a simplified version of a posteriori error estimation using the dual weighted residual (DWR) method. This method is used for the mesh adaption during the computation. The implementation using the software library package DOpElib and deal.II serves for the computation of different fluid-structure configurations.

Adaptive Multigrid Methods for Extended Fluid-Structure Interaction (eXFSI) Problem: Part I — Mathematical Modelling

2015 ◽  
Author(s):  
Bhuiyan Shameem Mahmood Ebna Hai ◽  
Markus Bause
Keyword(s):  
Finite Element ◽  
Wave Propagation ◽  
Variational Formulation ◽  
Fluid Structure Interaction ◽  
Multigrid Methods ◽  
Time Step ◽  
Fluid Structure ◽  
Structure Interaction ◽  
Time Stepping ◽  
Crank Nicolson

This contribution is the first part of three papers on Adaptive Multigrid Methods for eXtended Fluid-Structure Interaction (eXFSI) Problem, where we introduce a monolithic variational formulation and solution techniques. 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 of recent developments in the finite element approximation of FSI problem based on monolithic variational formulation in the well-established arbitrary Lagrangian Eulerian (ALE) framework. This research will focus on the newly developed mathematical model of a new FSI problem which is called eXtended Fluid-Structure Interaction (eXFSI) problem in ALE framework. This model is used to design an on-live Structural Health Monitoring (SHM) system in order to determine the wave propagation in moving domains and optimum locations for SHM sensors. eXFSI is strongly coupled problem of typical FSI with a wave propagation problem on the fluid-structure interface, where wave propagation problems automatically adopted the boundary conditions from of the typical FSI problem at each time step. The ALE approach provides a simple, but powerful procedure to couple fluid flows with solid deformations by a monolithic solution algorithm. In such a setting, the fluid equations are transformed to a fixed reference configuration via 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-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 an 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 Newton’s method whereas the spatial discretization is done with a Galerkin finite element scheme. To control computational costs we apply a simplified version of a posteriori error estimation using the dual weighted residual (DWR) method. This method is used for the mesh adaptation during the computation. The implementation is accomplished via the software library package DOpElib and deal.II for the computation of different eXFSI configurations.

scholarly journals A Monolithic Approach of Fluid–Structure Interaction by Discrete Mechanics

Fluids ◽  
2021 ◽  
Vol 6 (3) ◽  
pp. 95
Author(s):  
Stéphane Vincent ◽  
Jean-Paul Caltagirone
Keyword(s):  
Solid Mechanics ◽  
Mechanical Energy ◽  
Fluid Structure Interaction ◽  
Equation Of Motion ◽  
Discrete Equation ◽  
Discrete Mechanics ◽  
Fluid Structure ◽  
Structure Interaction ◽  
Vector Potentials

The unification of the laws of fluid and solid mechanics is achieved on the basis of the concepts of discrete mechanics and the principles of equivalence and relativity, but also the Helmholtz–Hodge decomposition where a vector is written as the sum of divergence-free and curl-free components. The derived equation of motion translates the conservation of acceleration over a segment, that of the intrinsic acceleration of the material medium and the sum of the accelerations applied to it. The scalar and vector potentials of the acceleration, which are the compression and shear energies, give the discrete equation of motion the role of conservation law for total mechanical energy. Velocity and displacement are obtained using an incremental time process from acceleration. After a description of the main stages of the derivation of the equation of motion, unique for the fluid and the solid, the cases of couplings in simple shear and uniaxial compression of two media, fluid and solid, make it possible to show the role of discrete operators and to find the theoretical results. The application of the formulation is then extended to a classical validation case in fluid–structure interaction.

Fluid–Structure Interaction of High Aspect-Ratio Hair-Like Micro-Structures Through Dimensional Transformation Using Lattice Boltzmann Method

2016 ◽  
Vol 08 (08) ◽  
pp. 1650095 ◽  
Author(s):  
H. Devaraj ◽  
Kean C. Aw ◽  
E. Haemmerle ◽  
R. Sharma
Keyword(s):  
Fluid Flow ◽  
Drag Force ◽  
Lattice Boltzmann ◽  
Stokes Equations ◽  
Fluid Structure Interaction ◽  
Structural Response ◽  
Momentum Exchange ◽  
Fluid Structure ◽  
Structure Interaction ◽  
Micro Structures

3D printed hair-like micro-structures have been previously demonstrated in a novel micro-fluidic flow sensor aimed at sensing air flows down to rates of a few milliliters per second. However, there is a lack of in-depth understanding of the structural response of these ‘micro-hairs' under a fluid flow field. This paper demonstrates the use of lattice Boltzmann methods (LBM) to understand this structural response towards a better optimization of the micro-hair flow sensors designed to suit the end applications' needs. The LBM approach was chosen as an efficient alternative to simulate Navier–Stokes equations for modeling fluid flow around complex geometries primarily for improved accuracy and simplicity with lesser computational costs. As the spatial dimensions of the sensor's flow channel are much larger in comparison to the actual micro-hairs (the sensing element), a multidimensional approach of combining two-dimensional (D2Q9) and three-dimensional (D3Q19) lattice configurations were implemented for improved computational speeds and efficiency. The drag force on the micro-hairs was estimated using the momentum-exchange method in the D3Q19 configuration and this drag force is transferred to the structural analysis model which determines the micro-hair deformation using Euler–Bernoulli beam theory. The entirety of the LBM Fluid–Structure Interaction (FSI) model was implemented within MATLAB and the obtained results are compared against the numerical model implemented on a commercially available software package.

Fluid-Structure Interaction Approach for Numerical Investigation of a Flexible Hydrofoil Deformations in Turbulent Fluid Flow

2018 ◽  
Author(s):  
M. Benaouicha ◽  
S. Guillou ◽  
A. Santa Cruz ◽  
H. Trigui
Keyword(s):  
Fluid Flow ◽  
Numerical Model ◽  
Stokes Equations ◽  
Fluid Structure Interaction ◽  
Time Step ◽  
Fluid Structure ◽  
Turbulent Fluid Flow ◽  
Turbulent Fluid ◽  
Structure Interaction ◽  
Ale Formulation

The study deals with a 3D Fluid-Structure Interaction (FSI) numerical model of a rectangular cantilevered flexible hydrofoil subjected to a turbulent fluid flow regime. The structural response and dynamic deformations are studied by analyzing the oscillations frequencies and amplitudes, under a hydrodynamics loads. The obtained numerical results are confronted with experimental ones, for validation. The numerical model is performed in the same geometric, physical and material conditions as the experimental set-up carried out in a hydrodynamic tunnel. A polyacetal (POM) flexible hydrofoil NACA0015 with an angle of attack of 8° is considered to be immersed in a fluid flow at a Reynold number of 3 × 105. The structure is initially at rest and then moved by the action of the fluid flow. The numerical model is based on a strong coupling procedure for solving the Fluid-Structure Interaction problem. The Arbitrary Lagrangian-Eulerian (ALE) formulation of the Navier-Stokes equations is used and an anisotropic diffusion equation is solved to compute the fluid mesh velocity and position at each time step. The finite volume method is used for the numerical resolution of the fluid dynamics equations. The structure deformations are described by the linear elasticity equation which is solved by the finite elements method. The Fluid-Structure coupled problem is solved by using the partitioned FSI implicit algorithm. A good agreement between numerical and experimental results for the hydrodynamics coefficients and hydrofoil deformations, maximum deflection and frequencies is obtained. The added mass and damping are analyzed and then the FSI effect on the dynamic deformations of the structure is highlighted.

Scalability study of an implicit solver for coupled fluid-structure interaction problems on unstructured meshes in 3D

2016 ◽  
Vol 32 (2) ◽  
pp. 207-219 ◽  
Author(s):  
Fande Kong ◽  
Xiao-Chuan Cai
Keyword(s):  
Stokes Equations ◽  
Fluid Structure Interaction ◽  
Three Dimensional ◽  
Coupled System ◽  
Fluid Structure ◽  
Structure Interaction ◽  
Krylov Method ◽  
Fine Mesh ◽  
Processor Cores ◽  
Fully Coupled

Fluid-structure interaction (FSI) problems are computationally very challenging. In this paper we consider the monolithic approach for solving the fully coupled FSI problem. Most existing techniques, such as multigrid methods, do not work well for the coupled system since the system consists of elliptic, parabolic and hyperbolic components all together. Other approaches based on direct solvers do not scale to large numbers of processors. In this paper, we introduce a multilevel unstructured mesh Schwarz preconditioned Newton–Krylov method for the implicitly discretized, fully coupled system of partial differential equations consisting of incompressible Navier–Stokes equations for the fluid flows and the linear elasticity equation for the structure. Several meshes are required to make the solution algorithm scalable. This includes a fine mesh to guarantee the solution accuracy, and a few isogeometric coarse meshes to speed up the convergence. Special attention is paid when constructing and partitioning the preconditioning meshes so that the communication cost is minimized when the number of processor cores is large. We show numerically that the proposed algorithm is highly scalable in terms of the number of iterations and the total compute time on a supercomputer with more than 10,000 processor cores for monolithically coupled three-dimensional FSI problems with hundreds of millions of unknowns.

scholarly journals FSI in Wind Turbines: A Review

2020 ◽  
Vol 8 (3) ◽  
pp. 37
Author(s):  
Yogesh Ramesh Patel
Keyword(s):  
Wind Turbine ◽  
Wind Turbines ◽  
Stokes Equations ◽  
Turbine Blades ◽  
Fluid Structure Interaction ◽  
Arbitrary Lagrangian Eulerian ◽  
Wind Turbine Blades ◽  
Fluid Structure ◽  
Structure Interaction ◽  
Deformable Structure

This paper provides a brief overview of the research in the field of Fluid-structure interaction in Wind Turbines. Fluid-Structure Interaction (FSI) is the interplay of some movable or deformable structure with an internal or surrounding fluid flow. Flow brought about vibrations of two airfoils used in wind turbine blades are investigated by using a strong coupled fluid shape interplay approach. The approach is based totally on a regularly occurring Computational Fluid Dynamics (CFD) code that solves the Navier-Stokes equations defined in Arbitrary Lagrangian-Eulerian (ALE) coordinates by way of a finite extent method. The need for the FSI in the wind Turbine system is studied and comprehensively presented.

scholarly journals Three-Dimensional Simulation of Fluid–Structure Interaction Problems Using Monolithic Semi-Implicit Algorithm

Fluids ◽  
2019 ◽  
Vol 4 (2) ◽  
pp. 94 ◽  
Author(s):  
Cornel Marius Murea
Keyword(s):  
Stokes Equations ◽  
Fluid Structure Interaction ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Arbitrary Lagrangian Eulerian ◽  
Time Step ◽  
Fluid Structure ◽  
Structure Interaction ◽  
Dimensional Simulation ◽  
Updated Lagrangian

A monolithic semi-implicit method is presented for three-dimensional simulation of fluid–structure interaction problems. The updated Lagrangian framework is used for the structure modeled by linear elasticity equation and, for the fluid governed by the Navier–Stokes equations, we employ the Arbitrary Lagrangian Eulerian method. We use a global mesh for the fluid–structure domain where the fluid–structure interface is an interior boundary. The continuity of velocity at the interface is automatically satisfied by using globally continuous finite element for the velocity in the fluid–structure mesh. The method is fast because we solve only a linear system at each time step. Three-dimensional numerical tests are presented.

Experimental and Numerical Analysis for Fluid-Structure Interaction for an Enclosed Hexagonal Assembly

2014 ◽  
Author(s):  
Lucia Sargentini ◽  
Benjamin Cariteau ◽  
Morena Angelucci
Keyword(s):  
Numerical Method ◽  
Stokes Equations ◽  
Interaction Analysis ◽  
Flow Behavior ◽  
Fluid Structure Interaction ◽  
Water Injection ◽  
Free Vibrations ◽  
Navier Stokes ◽  
Fluid Structure ◽  
Structure Interaction

This paper is related to fluid-structure interaction analysis of sodium cooled fast reactors core (Na-FBR). Sudden liquid evacuation between assemblies could lead to overall core movements (flowering and compaction) causing variations of core reactivity. The comprehension of the structure behavior during the evacuation could improve the knowledge about some SCRAMs for negative reactivity occurred in PHÉNIX reactor and could contribute on the study of the dynamic behavior of a FBR core. An experimental facility (PISE-2c) is designed composed by a Poly-methyl methacrylate hexagonal rods (2D-plan similitude with PHÉNIX assembly) with a very thin gap between assemblies. Another experimental device (PISE-1a) is designed and composed by a single hexagonal rod for testing the dynamic characteristics. Different experiments are envisaged: free vibrations and oscillations during water injection. A phenomenological analysis is reported showing the flow behavior in the gap and the structure response. Also computational simulations are presented in this paper. An efficient numerical method is used to solve Navier-Stokes equations coupled with structure dynamic equation. The numerical method is verified by the comparison of analytic models and experiments.

Linear Stability Analysis and Application of a New Solution Method of the Elastodynamic Equations Suitable for a Unified Fluid-Structure-Interaction Approach

2008 ◽  
Vol 130 (3) ◽  
Author(s):  
C. G. Giannopapa ◽  
G. Papadakis
Keyword(s):  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Solution Method ◽  
Stokes Equations ◽  
Fluid Structure Interaction ◽  
Analytic Solutions ◽  
Computational Domain ◽  
Fluid Structure ◽  
Structure Interaction

In the conventional approach for fluid-structure-interaction problems, the fluid and solid components are treated separately and information is exchanged across their interface. According to the conventional terminology, the current numerical methods can be grouped in two major categories: partitioned methods and monolithic methods. Both methods use separate sets of equations for fluid and solid that have different unknown variables. A unified solution method has been presented in the previous work of Giannopapa and Papadakis (2004, “A New Formulation for Solids Suitable for a Unified Solution Method for Fluid-Structure Interaction Problems,” ASME PVP 2004, San Diego, CA, July, PVP Vol. 491–1, pp. 111–117), which is different from these methods. The new approach treats both fluid and solid as a single continuum; thus, the whole computational domain is treated as one entity discretized on a single grid. Its behavior is described by a single set of equations, which are solved fully implicitly. In this paper, the elastodynamic equations are reformulated so that they contain the same unknowns as the Navier–Stokes equations, namely, velocities and pressure. Two time marching and one spatial discretization scheme, widely used for fluid equations, are applied for the solution of the reformulated equations for solids. Using linear stability analysis, the accuracy and dissipation characteristics of the resulting difference equations are examined. The aforementioned schemes are applied to a transient structural problem (beam bending) and the results compare favorably with available analytic solutions and are consistent with the conclusions of the stability analysis. A parametric investigation using different meshes, time steps, and beam dimensions is also presented. For all cases examined, the numerical solution was stable and robust and therefore is suitable for the next stage of application to full fluid-structure-interaction problems.

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