Monolithic Fluid-structure Interaction Research Articles

Computational fluid–structure interaction framework for passive feathering and cambering in flapping insect wings

AbstractIn flapping insect wings, veins support flexible wing membranes such that the wings form feathering and cambering motions passively from large elastic deformations. These motions are essentially important in unsteady aerodynamics of insect flapping flight. Hence, the underlying mechanism of this phenomenon is an important issue in studies on insect flight. Systematic parametric studies on strong coupling between a model wing describing these elastic deformations and the surrounding fluid, which is a direct formulation of this phenomenon, will be effective for solving this issue. The purpose of this study is to develop a robust numerical framework for these systematic parametric studies. The proposed framework consists of two novel numerical methods: (1) A fully parallelized solution method using both algebraic splitting and semi‐implicit scheme for monolithic fluid–structure interaction (FSI) equation systems, which is numerically stable for a wide range of properties such as solid‐to‐fluid mass ratios and large body motions, and large elastic deformations. (2) A structural mechanics model for insect flapping wings using pixel modeling (pixel model wing), which is combined with explicit node‐positioning to reduce computational costs significantly in controlling fluid meshes. The validity of the proposed framework is demonstrated for some benchmark problems and a dynamically scaled model incorporating actual insect data. Finally, from a parametric study for the pixel model wing flapped in fluid with a wide range of solid‐to‐fluid mass ratios, we find a FSI mechanism of feathering and cambering motions in flapping insect wings.

Modeling and simulation of thin-walled piezoelectric energy harvesters immersed in flow using monolithic fluid–structure interaction

A monolithic numerical scheme for fluid–structure interaction with special interest in thin-walled piezoelectric energy harvesters driven by fluid is proposed. Employing a beam/shell model for the thin-walled structure in this particular application creates a FSI problem in which an ( n − 1 ) -dimensional structure is embedded in an n -dimensional fluid flow. This choice induces a strongly discontinuous pressure field along the moving fluid–solid interface. We overcome this challenge within a continuous finite element framework by a splitting-fluid-domain approach. The governing equations of the multiphysics problem are solved in a simultaneous fashion in order to reliably capture the main dynamic characteristics of the strongly-coupled system that involves a large deformation piezoelectric composite structure, an integrated electric circuit and an incompressible viscous fluid. The monolithic solution scheme is based on the weighted residuals method, with the boundary-fitted finite element method used for the discretization in space, and the generalized- α method for discretization in time. The proposed framework is evaluated against reference data of two popular FSI benchmark problems. Two additional numerical examples of flow-driven thin-walled piezoelectric energy harvesters demonstrate the feasibility of the framework to predict controlled cyclic response and limit-cycle oscillations and thus the power output in typical operational states of this class of energy harvesting devices. • A fully monolithic model tailored to flow-driven thin-walled piezoelectric energy harvesters (PEHs). • A novel method to tackle the strongly discontinuous pressure field of the fluid field. • The computational framework is validated against classical FSI benchmark problems. • The importance of optimized PEH electrode coverage is revealed by two new benchmarks. • Reference implementation using the open-source finite element framework FEniCS.

Eulerian finite volume formulation using Lagrangian marker particles for incompressible fluid–structure interaction problems

AbstractWe propose a monolithic fluid–structure interaction (FSI) method that uses the cell‐centered finite volume formulation in the Eulerian description, Lagrangian marker particles allocated in the solid region, and the incompressible mixture formulation. In the proposed method, we compute all the basic equations and spatial derivatives, except the solid constitutive equations, on an Eulerian mesh to avoid neighboring particle search. Although full Eulerian methods that use a Cartesian mesh are attractive for FSI problems that require large‐scale computing and include complex geometries and the large deformation of the solid, they cannot avoid the numerical dissipation of the interfaces or internal variables of the solid caused by their advection. This computational problem has been a barrier to the industrial application of full Eulerian mesh methods. In the numerical examples, we confirmed that the proposed method retains sharp interfaces, such as the corners of a square solid, and yields more accurate numerical results for the deformation, energy, and incompressibility of a solid in fluid than our conventional Eulerian FSI method.

Coupling of IGA and peridynamics for air-blast fluid-structure interaction using an immersed approach

We present a novel formulation based on an immersed coupling of Isogeometric Analysis (IGA) and Peridynamics (PD) for the simulation of fluid-structure interaction (FSI) phenomena for air blast. We aim to develop a practical computational framework that is capable of capturing the mechanics of air blast coupled to solids and structures that undergo large, inelastic deformations with extreme damage and fragmentation. An immersed technique is used, which involves an a priori monolithic FSI formulation with the implicit detection of the fluid-structure interface and without limitations on the solid domain motion. The coupled weak forms of the fluid and structural mechanics equations are solved on the background mesh. Correspondence-based PD is used to model the meshfree solid in the foreground domain. We employ the Non-Uniform Rational B-Splines (NURBS) IGA functions in the background and the Reproducing Kernel Particle Method (RKPM) functions for the PD solid in the foreground. We feel that the combination of these numerical tools is particularly attractive for the problem class of interest due to the higher-order accuracy and smoothness of IGA and RKPM, the benefits of using immersed methodology in handling the fluid-structure coupling, and the capabilities of PD in simulating fracture and fragmentation scenarios. Numerical examples are provided to illustrate the performance of the proposed air-blast FSI framework.

Vortex-induced vibrations: a soft coral feeding strategy?

Abstract

Fluid-structure interaction with H(div)-conforming finite elements

In this paper a novel application of the (high-order) H(div)-conforming Hybrid Discontinuous Galerkin finite element method for monolithic fluid-structure interaction (FSI) is presented. The Arbitrary Lagrangian Eulerian (ALE) description is derived for H(div)-conforming finite elements including the Piola transformation, yielding exact divergence free fluid velocity solutions. The arising method is demonstrated by means of the benchmark problems proposed by Turek and Hron (2006). With hp-refinement strategies singularities and boundary layers are overcome leading to optimal spatial convergence rates.

Numerical study on hydroelastic interaction between solitary wave and submerged box

The nonlinear hydroelastic interaction between a solitary wave and a submerged box with elastic upper surface plate is investigated in a 2D numerical wave flume. The objective is to investigate how hydroelasticity affects the interaction process. The numerical wave flume solves incompressible Navier-Stokes equations with a Volume-of-Fluid method for free surface simulation. The linear elastic structure dynamic equations are solved by a Finite Element Method, and embedded into the solution of flow field by using a monolithic fluid-structure interaction algorithm. The numerical method is thoroughly verified against existing experiments and numerical simulations. A series of numerical tests are conducted, which contains free vibrations of the plate, and the interaction between solitary waves and submerged boxes with various wave amplitudes and submerged depths. Results obtained with and without considering hydroelasticity are compared to investigate the influence of hydroelastic effect on the wave load, the structure response and the flow field. Fast Fourier Transform and wavelet transform are adopted to reveal the oscillatory features of the interaction process. Some meaningful conclusions are drawn, such as hydroelasticity changes the amplitude and period of the oscillatory motion and the variation of the oscillatory frequency can be approximated by a simple still water prediction method.

A class of analytic solutions for verification and convergence analysis of linear and nonlinear fluid-structure interaction algorithms

Fluid-structure interaction (FSI) problems are pervasive in the computational engineering community. The need to address challenging FSI problems has led to the development of a broad range of numerical methods addressing a variety of application-specific demands. While a range of numerical and experimental benchmarks are present in the literature, few solutions are available that enable both verification and spatiotemporal convergence analysis. In this paper, we introduce a class of analytic solutions to FSI problems involving shear in channels and pipes. Comprised of 16 separate analytic solutions, our approach is permuted to enable progressive verification and analysis of FSI methods and implementations, in two and three dimensions, for static and transient scenarios as well as for linear and hyperelastic solid materials. Results are shown for a range of analytic models exhibiting progressively complex behavior. The utility of these solutions for analysis of convergence behavior is further demonstrated using a previously published monolithic FSI technique. The resulting class of analytic solutions addresses a core challenge in the development of novel FSI algorithms and implementations, providing a progressive testbed for verification and detailed convergence analysis.

A monolithic approach to fluid‐structure interaction based on a hybrid Eulerian‐ALE fluid domain decomposition involving cut elements

SummaryA novel method for complex fluid‐structure interaction (FSI) involving large structural deformation and motion is proposed. The new approach is based on a hybrid fluid formulation that combines the advantages of purely Eulerian (fixed‐grid) and arbitrary Lagrangian‐Eulerian (ALE) moving mesh formulations in the context of FSI. The structure, as commonly given in Lagrangian description, is surrounded by a fine resolved layer of fluid elements based on an ALE‐framework. This ALE‐fluid patch, which is embedded in a Eulerian background fluid domain, follows the deformation and motion of the structural interface. This approximation technique is not limited to finite element methods but can also be realized within other frameworks like finite volume or discontinuous Galerkin methods. In this work, the surface coupling between the two disjoint fluid subdomains is imposed weakly using a stabilized Nitsche's technique in a cut finite element method (CutFEM) framework. At the fluid‐solid interface, standard weak coupling of node‐matching or nonmatching finite element approximations can be utilized. As the fluid subdomains can be meshed independently, a sufficient mesh quality in the vicinity of the common fluid‐structure interface can be assured. To our knowledge, the proposed method is the only method (despite some overlapping domain decomposition approaches that suffer from other issues) that allows for capturing boundary layers and flow detachment via appropriate grids around largely moving and deforming bodies. In contrast to other methods, it is possible to do this, eg, without the necessity of costly remeshing procedures. A clear advantage over existing overlapping domain decomposition methods consists in the sharp splitting of the fluid domain, which comes along with improved convergence behavior of the resulting monolithic FSI system. In addition, it might also help to save computational costs as now background grids can be much coarser. Various FSI‐cases of rising complexity conclude the work. For validation purpose, results have been compared to simulations using a classical ALE‐fluid description or purely fixed‐grid CutFEM‐based schemes.

A monolithic fluid–structure interaction formulation for solid and liquid membranes including free-surface contact

A unified fluid–structure interaction (FSI) formulation is presented for solid, liquid and mixed membranes. Nonlinear finite elements (FE) and the generalized-α scheme are used for the spatial and temporal discretization. The membrane discretization is based on curvilinear surface elements that can describe large deformations and rotations, and also provide a straightforward description for contact. The fluid is described by the incompressible Navier–Stokes equations, and its discretization is based on stabilized Petrov–Galerkin FE. The coupling between fluid and structure uses a conforming sharp interface discretization, and the resulting non-linear FE equations are solved monolithically within the Newton–Raphson scheme. An arbitrary Lagrangian–Eulerian formulation is used for the fluid in order to account for the mesh motion around the structure. The formulation is very general and admits diverse applications that include contact at free surfaces. This is demonstrated by two analytical and three numerical examples exhibiting strong coupling between fluid and structure. The examples include balloon inflation, droplet rolling and flapping flags. They span a Reynolds-number range from 0.001 to 2000. One of the examples considers the extension to rotation-free shells using isogeometric FE.

A new formulation for air-blast fluid–structure interaction using an immersed approach. Part I: basic methodology and FEM-based simulations

In this two-part paper we begin the development of a new class of methods for modeling fluid–structure interaction (FSI) phenomena for air blast. We aim to develop accurate, robust, and practical computational methodology, which is capable of modeling the dynamics of air blast coupled with the structure response, where the latter involves large, inelastic deformations and disintegration into fragments. An immersed approach is adopted, which leads to an a-priori monolithic FSI formulation with intrinsic contact detection between solid objects, and without formal restrictions on the solid motions. In Part I of this paper, the core air-blast FSI methodology suitable for a variety of discretizations is presented and tested using standard finite elements. Part II of this paper focuses on a particular instantiation of the proposed framework, which couples isogeometric analysis (IGA) based on non-uniform rational B-splines and a reproducing-kernel particle method (RKPM), which is a Meshfree technique. The combination of IGA and RKPM is felt to be particularly attractive for the problem class of interest due to the higher-order accuracy and smoothness of both discretizations, and relative simplicity of RKPM in handling fragmentation scenarios. A collection of mostly 2D numerical examples is presented in each of the parts to illustrate the good performance of the proposed air-blast FSI framework.

A new formulation for air-blast fluid–structure interaction using an immersed approach: part II—coupling of IGA and meshfree discretizations

In this two-part paper we begin the development of a new class of methods for modeling fluid---structure interaction (FSI) phenomena for air blast. We aim to develop accurate, robust, and practical computational methodology, which is capable of modeling the dynamics of air blast coupled with the structure response, where the latter involves large, inelastic deformations and disintegration into fragments. An immersed approach is adopted, which leads to an a-priori monolithic FSI formulation with intrinsic contact detection between solid objects, and without formal restrictions on the solid motions. In Part I of this paper, the core air-blast FSI methodology suitable for a variety of discretizations is presented and tested using standard finite elements. Part II of this paper focuses on a particular instantiation of the proposed framework, which couples isogeometric analysis (IGA) based on non-uniform rational B-splines and a reproducing-kernel particle method (RKPM), which is a meshfree technique. The combination of IGA and RKPM is felt to be particularly attractive for the problem class of interest due to the higher-order accuracy and smoothness of both discretizations, and relative simplicity of RKPM in handling fragmentation scenarios. A collection of mostly 2D numerical examples is presented in each of the parts to illustrate the good performance of the proposed air-blast FSI framework.

Fluid-structure interaction including volumetric coupling with homogenised subdomains for modeling respiratory mechanics.

In this article, a novel approach is presented for combining standard fluid-structure interaction with additional volumetric constraints to model fluid flow into and from homogenised solid domains. The proposed algorithm is particularly interesting for investigations in the field of respiratory mechanics as it enables the mutual coupling of airflow in the conducting part and local tissue deformation in the respiratory part of the lung by means of a volume constraint. In combination with a classical monolithic fluid-structure interaction approach, a comprehensive model of the human lung can be established that will be useful to gain new insights into respiratory mechanics in health and disease. To illustrate the validity and versatility of the novel approach, three numerical examples including a patient-specific lung model are presented. The proposed algorithm proves its capability of computing clinically relevant airflow distribution and tissue strain data at a level of detail that is not yet achievable, neither with current imaging techniques nor with existing computational models. Copyright © 2016 John Wiley & Sons, Ltd.

A penalty-projection algorithm for a monolithic fluid-structure interaction solver

In this paper we propose a new iterative penalty-projection algorithm for a monolithic fluid-structure interaction solver. Projection methods, that split the computation of the velocity from the pressure, are very popular in fluid dynamics since the boundary errors generated by the projection method are localized mainly near the boundary layers where the incorrect pressure boundary conditions are imposed. However, when solid regions are taken into account, the pressure projected field cannot satisfy fully coupled boundary constraints imposed on external solid surfaces such as stress-free conditions, and, due to the rigidity of the medium, the boundary errors propagate deeply in the interior. In order to reduce the projection errors we propose a one-step penalty-projection method in the fluid domain and an iterative penalty-projection method in the solid region. This technique decouples the pressure-velocity degrees of freedom and, as a consequence, the computational cost. In order to verify the accuracy and robustness of the proposed method we compare the results between this splitting velocity-pressure algorithm and the coupled one. These numerical results show stability and robustness of the proposed algorithm with a strong reduction of the computational effort. A new penalty-projection algorithm for a monolithic FSI solver is proposed.Projection method error is localized where pressure boundary conditions are imposed.A one-step penalty together with an iterative projection algorithm is used.This technique reduces the problem degrees of freedom and the computational cost.Numerical results show stability and reduction of cpu effort for large problems.

A Parallel Implementation of a Two-Level Overlapping Schwarz Method with Energy-Minimizing Coarse Space Based on Trilinos

We describe a new implementation of a two-level overlapping Schwarz preconditioner with energy-minimizing coarse space (GDSW: generalized Dryja--Smith--Widlund) and show numerical results for an additive and a hybrid additive-multiplicative version. Our parallel implementation makes use of the Trilinos software library and provides a framework for parallel two-level Schwarz methods. We show parallel scalability for two- and three-dimensional scalar second-order elliptic and linear elasticity problems for several thousands of cores. We also discuss techniques for the parallel construction of coarse spaces which are also of interest for other parallel preconditioners and discretization methods using energy minimizing coarse functions. We finally show an application in monolithic fluid-structure interaction, where significant improvements are achieved compared to a standard algebraic, one-level overlapping Schwarz method.

A preliminary investigation of the growth of an aneurysm with a multiscale monolithic Fluid-Structure interaction solver

In this work we investigate the potentialities of multi-scale engineering techniques to approach complex problems related to biomedical and biological fields. In particular we study the interaction between blood and blood vessel focusing on the presence of an aneurysm. The study of each component of the cardiovascular system is very difficult due to the fact that the movement of the fluid and solid is determined by the rest of system through dynamical boundary conditions. The use of multi-scale techniques allows us to investigate the effect of the whole loop on the aneurysm dynamic. A three-dimensional fluid-structure interaction model for the aneurysm is developed and coupled to a mono-dimensional one for the remaining part of the cardiovascular system, where a point zero-dimensional model for the heart is provided. In this manner it is possible to achieve rigorous and quantitative investigations of the cardiovascular disease without loosing the system dynamic. In order to study this biomedical problem we use a monolithic fluid-structure interaction (FSI) model where the fluid and solid equations are solved together. The use of a monolithic solver allows us to handle the convergence issues caused by large deformations. By using this monolithic approach different solid and fluid regions are treated as a single continuum and the interface conditions are automatically taken into account. In this way the iterative process characteristic of the commonly used segregated approach, it is not needed any more.

A combined fluid–structure interaction and multi–field scalar transport model for simulating mass transport in biomechanics

SUMMARYMass transport processes are known to play an important role in many fields of biomechanics such as respiratory, cardiovascular, and biofilm mechanics. In this paper, we present a novel computational model considering the effect of local solid deformation and fluid flow on mass transport. As the transport processes are assumed to influence neither structure deformation nor fluid flow, a sequential one‐way coupling of a fluid–structure interaction (FSI) and a multi‐field scalar transport model is realized. In each time step, first the non‐linear monolithic FSI problem is solved to determine current local deformations and velocities. Using this information, the mass transport equations can then be formulated on the deformed fluid and solid domains. At the interface, concentrations are related depending on the interfacial permeability. First numerical examples demonstrate that the proposed approach is suitable for simulating convective and diffusive scalar transport on coupled, deformable fluid and solid domains. Copyright © 2014 John Wiley & Sons, Ltd.

A COMPRESSIBLE LAGRANGIAN FRAMEWORK FOR MODELING THE FLUID–STRUCTURE INTERACTION IN THE UNDERWATER IMPLOSION OF AN ALUMINUM CYLINDER

We propose a fully Lagrangian monolithic system for the simulation of the underwater implosion of cylindrical aluminum containers. A variationally stabilized form of the Lagrangian shock hydrodynamics is exploited to deal with the ultrahigh compression shock waves that travel in both air and water domains. The aluminum cylinder, which separates the internal atmospheric-pressure air from the external high-pressure water, is modeled by a three-node rotation-free shell element. The cylinder undergoes fast transient deformations, large enough to produce self-contact along it. A novel elastic frictionless contact model is used to detect contact and compute the non-penetrating forces in the discretized domain between the mid-planes of the shell. Mesh quality in the vicinity of the cylinder is guaranteed by regenerating the mesh in the air and water domains when large displacements occur. A monolithic fluid–structure interaction (FSI) system is then solved. Two schemes are tested, implicit using the predictor/multi-corrector Bossak scheme, and explicit, using the forward Euler scheme. The results of the two simulations are compared with experimental data.

Special Issue on Computational Fluid Mechanics and Fluid–Structure Interaction Preface

This special issue is a collection of the papers contributed by authors who were invited to speak at the symposium on Computational Methods for Fluid–Structure Interaction, ASME International Mechanical Engineering Congress and Exposition, Vancouver, Canada, November 12–18, 2010. The symposium was organized by Yuri Bazilevs (University of California, San Diego), Kenji Takizawa (Waseda University, Tokyo), and Tayfun Tezduyar (Rice University).The special issue contains papers on advances in computational methods for computational fluid dynamics (CFD) and fluid–structure interaction (FSI). FSI is one of the most important classes of multiphysics problems in modern mechanics. It is currently receiving much attention from the academic community, national laboratories, and the industrial sector.The papers mostly focus on moving-grid methods, such as the arbitrary Lagrangian–Eulerian and space–time formulations. The methods discussed address the challenges of coupling rigid objects and free-surface flow, coupling of acoustic fluids and structures using a monolithic FSI approach, and coupling of discrete element and finite element methods in the context of particulate flows.The special issue contains papers on advances in patient-specific cardiovascular hemodynamics, FSI modeling of parachutes, air turbine aerodynamics, aerodynamics of flapping wings, ship hydrodynamics, liquid sloshing in tanks, and turbulence in the upper ocean. Low-order finite element method is the dominant spatial discretization technique in most of the special issue articles. However, spatial and temporal higher-order NURBS-based discretizations, such as those employed in isogeometric analysis, are also discussed and are found to increase the accuracy and robustness of the computations. One of the articles provides the methodology and background mathematical theory for how to correctly define boundary fluxes in coupled multiphysics simulations.We would like to thank the authors for their efforts in preparing the special issue articles, and for meeting the special issue deadlines. These contributions will undoubtedly help advance the fields of CFD and FSI.

A symmetric positive definite formulation for monolithic fluid structure interaction

In this paper we consider a strongly coupled (monolithic) fluid structure interaction framework for incompressible flow, as opposed to a loosely coupled (partitioned) method. This requires solving a single linear system that combines the unknown velocities of the structure with the unknown pressures of the fluid. In our previous work, we were able to obtain a symmetric formulation of this coupled system; however, it was also indefinite, making it more difficult to solve. In fact in practice there have been cases where we have been unable to invert the system. In this paper we take a novel approach that consists of factoring the damping matrix of deformable structures and show that this can be used to obtain a symmetric positive definite system, at least to the extent that the uncoupled systems were symmetric positive definite. We use a traditional MAC grid discretization of the fluid and a fully Lagrangian discretization of the structures for the sake of exposition, noting that our procedure can be generalized to other scenarios. For the special case of rigid bodies, where there are no internal damping forces, we exactly recover the system of Batty et al. (2007) [4].