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Numerical Methods for FluidStructure Interaction  A Review
, 2012
"... The interactions between incompressible fluid flows and immersed structures are nonlinear multiphysics phenomena that have applications to a wide range of scientific and engineering disciplines. In this article, we review representative numerical methods based on conforming and nonconforming me ..."
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The interactions between incompressible fluid flows and immersed structures are nonlinear multiphysics phenomena that have applications to a wide range of scientific and engineering disciplines. In this article, we review representative numerical methods based on conforming and nonconforming meshes that are currently available for computing fluidstructure interaction problems, with an emphasis on some of the recent developments in the field. A goal is to categorize the selected methods and assess their accuracy and efficiency. We discuss challenges faced by researchers in this field, and we emphasize the importance of interdisciplinary effort for advancing the study in fluidstructure interactions.
Numerically Stable FluidStructure Interactions Between Compressible Flow and Solid Structures
"... We propose a novel method to implicitly twoway couple Eulerian compressible flow to volumetric Lagrangian solids. The method works for both deformable and rigid solids and for arbitrary equations of state. The method exploits the formulation of [11] which solves compressible fluid in a semiimplici ..."
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We propose a novel method to implicitly twoway couple Eulerian compressible flow to volumetric Lagrangian solids. The method works for both deformable and rigid solids and for arbitrary equations of state. The method exploits the formulation of [11] which solves compressible fluid in a semiimplicit manner, solving for the advection part explicitly and then correcting the intermediate state to time tn+1 using an implicit pressure, obtained by solving a modified Poisson system. Similar to previous fluidstructure interaction methods, we apply pressure forces to the solid and enforce a velocity boundary condition on the fluid in order to satisfy a noslip constraint. Unlike previous methods, however, we apply these coupled interactions implicitly by adding the constraint to the pressure system and combining it with any implicit solid forces in order to obtain a strongly coupled, symmetric indefinite system (similar to [17], which only handles incompressible flow). We also show that, under a few reasonable assumptions, this system can be made symmetric positivedefinite by following the methodology of [16]. Because our method handles the fluidstructure interactions implicitly, we avoid introducing any new time step restrictions and obtain stable results even for high densitytomass ratios, where explicit methods struggle or fail. We exactly conserve momentum and kinetic energy (thermal fluidstructure interactions are not considered) at the fluidstructure interface, and hence naturally handle highly nonlinear phenomenon such as shocks, contacts and rarefactions. 1.
Geometry of unsteady fluid transport during fluidstructure interactions
 J. Fluid Mech
"... fluid–structure interactions ..."
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On dynamic mode decomposition: theory and applications,” arXiv preprint arXiv:1312.0041
, 2013
"... Abstract. Originally introduced in the fluid mechanics community, dynamic mode decomposition (DMD) has emerged as a powerful tool for analyzing the dynamics of nonlinear systems. However, existing DMD theory deals primarily with sequential time series for which the measurement dimension is much lar ..."
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Cited by 6 (4 self)
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Abstract. Originally introduced in the fluid mechanics community, dynamic mode decomposition (DMD) has emerged as a powerful tool for analyzing the dynamics of nonlinear systems. However, existing DMD theory deals primarily with sequential time series for which the measurement dimension is much larger than the number of measurements taken. We present a theoretical framework in which we define DMD as the eigendecomposition of an approximating linear operator. This generalizes DMD to a larger class of datasets, including nonsequential time series. We demonstrate the utility of this approach by presenting novel sampling strategies that increase computational efficiency and mitigate the effects of noise, respectively. We also introduce the concept of linear consistency, which helps explain the potential pitfalls of applying DMD to rankdeficient datasets, illustrating with examples. Such computations are not considered in the existing literature, but can be understood using our more general framework. In addition, we show that our theory strengthens the connections between DMD and Koopman operator theory. It also establishes connections between DMD and other techniques, including the eigensystem realization algorithm (ERA), a system identification method, and linear inverse modeling (LIM), a method from climate science. We show that under certain conditions, DMD is equivalent to LIM.
Numerical simulations of fiber sedimentation in NavierStokes flows
 J. Comput. Phys
"... Abstract. We perform numerical simulations of the sedimentation of rigid fibers suspended in a viscous incompressible fluid at nonzero Reynolds numbers. The fiber sedimentation system is modeled as a twodimensional immersed boundary problem, which naturally accommodates the fluidparticle interac ..."
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Cited by 5 (1 self)
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Abstract. We perform numerical simulations of the sedimentation of rigid fibers suspended in a viscous incompressible fluid at nonzero Reynolds numbers. The fiber sedimentation system is modeled as a twodimensional immersed boundary problem, which naturally accommodates the fluidparticle interactions and which allows the simulation of a large number of suspending fibers. We study the dynamics of sedimenting fibers under a variety of conditions, including differing fiber densities, Reynolds numbers, domain boundary conditions, etc. Simulation results are compared to experimental measurements and numerical results obtained in previous studies. AMS subject classifications: 76D05, 76M25 Key words: Fiber sedimentation, immersed boundaries, NavierStokes equations.
Modeling the unsteady aerodynamic forces on smallscale wings
"... The goal of this work is to develop low order dynamical systems models for the unsteady aerodynamic forces on small wings and to better understand the physical characteristics of unsteady laminar separation. Reduced order models for a fixed, high angle of attack flat plate are obtained through Galer ..."
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The goal of this work is to develop low order dynamical systems models for the unsteady aerodynamic forces on small wings and to better understand the physical characteristics of unsteady laminar separation. Reduced order models for a fixed, high angle of attack flat plate are obtained through Galerkin projection of the governing NavierStokes equations onto POD modes. Projected models are compared with direct numerical simulation (DNS) to show that they preserve qualitative behavior such as coherent structures. It is shown that in flows with Reynolds number 100, even a two degree of freedom model is sufficient to capture high angle of attack laminar vortex shedding. Next, the classical theories of Theodorsen and Wagner are compared with DNS for a number of pitch and plunge maneuvers of varying Strouhal number, reduced frequency, pitch amplitude and center. In addition to determining when these theories break down, the flow field structures are investigated to determine how the theories break down. This is an important first step toward combining and extending classical unsteady aerodynamic models to include high angle of attack effects. Theodorsen’s model for the lift of a sinusoidally pitching or plunging plate is shown to agree moderately well with DNS for reduced frequencies k < 2.0. One major observation is that the classical aerodynamic models all begin to disagree when the effective angle of attack, either determined by Strouhal number in the plunging case or angle of attack excursion in the pitching case, exceeds the critical stall angle where vortex shedding and laminar separation become prominent. Velocity field and body force data for a flat plate are generated by 2D direct numerical simulation using an immersed boundary method for Reynolds number 100300, and regions of separated flow and wake structures are visualized using Finite Time Lyapunov Exponents (FTLE) fields, the ridges of which are Lagrangian coherent structures (LCS). I.
A fractional step immersed boundary method for stokes flow with an inextensible interface enclosing a solid particle
 SIAM J. Sci. Comput
"... Abstract. In this paper, we develop a fractional step method based on the immersed boundary (IB) formulation for Stokes flow with an inextensible (incompressible) interface enclosing a solid particle. In addition to solving for the fluid variables such as the velocity and pressure, the present probl ..."
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Abstract. In this paper, we develop a fractional step method based on the immersed boundary (IB) formulation for Stokes flow with an inextensible (incompressible) interface enclosing a solid particle. In addition to solving for the fluid variables such as the velocity and pressure, the present problem involves finding an extra unknown elastic tension such that the surface divergence of the velocity is zero along the interface, and an extra unknown particle surface force such that the velocity satisfies the noslip boundary condition along the particle surface. While the interface moves with local fluid velocity, the enclosed particle hereby undergoes a rigid body motion, and the system is closed by the forcefree and torquefree conditions along the particle surface. The equations are then discretized by standard centered difference schemes on a staggered grid, and the interactions between the interface and particle with the fluid are discretized using a discrete delta function as in the IB method. The resultant linear system of equations is symmetric and can be solved by fractional steps so that only fast Poisson solvers are involved. The present method can be extended to Navier– Stokes flow with moderate Reynolds number by treating the nonlinear advection terms explicitly for the time integration. The convergent tests for a Stokes solver with or without an inextensible interface are performed and confirm the desired accuracy. The tanktreading to tumbling motion for an inextensible interface enclosing a solid particle with different filling fractions under a simple shear flow has been studied extensively, and the results here are in good agreement with those obtained in literature.
D.R.: Lift enhancement for lowaspectratio wings with periodic excitation
 AIAA J
"... In an effort to enhance lift on lowaspectratio rectangular flatplate wings in lowReynoldsnumber poststall flows, periodic injection of momentum is considered along the trailing edge in this numerical study. The purpose of actuation is not to reattach the flowbut to change the dynamics of thewak ..."
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In an effort to enhance lift on lowaspectratio rectangular flatplate wings in lowReynoldsnumber poststall flows, periodic injection of momentum is considered along the trailing edge in this numerical study. The purpose of actuation is not to reattach the flowbut to change the dynamics of thewake vortices such that the resulting lift force is increased. Periodic forcing is observed to be effective in increasing lift for various aspect ratios and angles of attack, achieving a similar lift enhancement attained by steady forcingwith lessmomentum input. Through the investigation on the influence of the actuation frequency, it is also found that there exists a frequency at which the flow locks on to a timeperiodic highlift state. Nomenclature AR = aspect ratio b = span CD = drag coefficient CL = lift coefficient C = steady momentum coefficient hCi = oscillatory momentum coefficient c = chord Fx, Fy = drag and lift forces F = nondimensional actuation frequency ( fL=U1) f = actuation frequency fact = actuator force f̂act = actuator force scaling vector fbdry = boundary force fn = natural shedding frequency L = characteristic length of separation p = pressure Q = Q criterion Re = Reynolds number ( U1c=) St = Strouhal number ( fnc sin=U1) s = material coordinate t = time U1 = freestream velocity u = velocity vector uact = actuator velocity x = streamwise, vertical, and spanwise coordinates, x; y; z x0; y0 = actuator position = angle of attack = Heaviside step function t = time step x = grid resolution ~ = regularized delta function = Lagrangian coordinate = kinematic viscosity = density = actuator slot width = phase! = vorticity vector
Fournier: A Second Order Penalized Direct Forcing for Hybrid Cartesian/Immersed Boundary Flow Simulations
 In progress
, 2012
"... interpolation scheme Abstract. Flows around complex stationary/moving solids take an important place in lifescience context or in many engineering applications. Usually, these problems are solved by bodyfitted approaches on unstructured meshes with boundary conditions directly imposed on the domai ..."
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interpolation scheme Abstract. Flows around complex stationary/moving solids take an important place in lifescience context or in many engineering applications. Usually, these problems are solved by bodyfitted approaches on unstructured meshes with boundary conditions directly imposed on the domain boundary. Another way is using immersed boundary (IB) techniques: the physical domain is immersed in a fixed fictitious one of simpler geometry on Cartesian grids. It allows to use efficient, fast and accurate numerical methods avoiding the tedious task of remeshing in case of time varying geometry. In contrast, one needs specific methods to take into account the IB conditions (IBC). Here, we propose a second order penalized direct forcing method for unsteady incompressible flows with Dirichlet’s IBC. It consists in adding a penalized forcing term to the initial problem, applied only on Cartesian nodes near the IB, in order to bring back the variable to the imposed one. Regarding NavierStokes solvers using a projection scheme, the forcing term is distributed both in the velocity prediction and in the correction equations. It leads to a natural way to prescribe the pressure boundary conditions around obstacles. Numerical experiments, performed for laminar flows around static/moving solids, assess the validity and illustrate the ability of our method, showing in particular a quadratic convergence rate. ha l0