Results 1  10
of
73
An adaptive, formally second order accurate version of the immersed boundary method
, 2006
"... ..."
Penalty immersed boundary method for an elastic boundary with mass
 Physics of Fluids
"... The immersed boundary (IB) method has been widely applied to problems involving a moving elastic boundary that is immersed in fluid and interacting with it. But most of the previous applications of the IB method have involved a massless elastic boundary and used efficient Fourier transform methods f ..."
Abstract

Cited by 22 (3 self)
 Add to MetaCart
(Show Context)
The immersed boundary (IB) method has been widely applied to problems involving a moving elastic boundary that is immersed in fluid and interacting with it. But most of the previous applications of the IB method have involved a massless elastic boundary and used efficient Fourier transform methods for the numerical solutions. Extending the method to cover the case of a massive boundary has required spreading the boundary mass out onto the fluid grid and then solving the NavierStokes equations with a variable mass density. The variable mass density of this previous approach makes Fourier transform methods inapplicable, and requires a multigrid solver. Here we propose a new and simple way to give mass to the elastic boundary and show that the new method can be applied to many problems for which the boundary mass is important. The new method does not spread mass to the fluid grid, retains the use of Fourier transform methodology, and is easy to implement in the context of an existing IB method code for the massless case.
A Finite Element Approach to the Immersed Boundary Method
, 2004
"... The immersed boundary method was introduced by Peskin in [31] to study the blood flow in the heart and further applied to many situations where a fluid interacts with an elastic structure. The basic idea is to consider the structure as a part of the fluid where additional forces are applied and addi ..."
Abstract

Cited by 19 (7 self)
 Add to MetaCart
(Show Context)
The immersed boundary method was introduced by Peskin in [31] to study the blood flow in the heart and further applied to many situations where a fluid interacts with an elastic structure. The basic idea is to consider the structure as a part of the fluid where additional forces are applied and additional mass is localized. The forces exerted by the structure on the fluid are taken into account as a source term in the NavierStokes equations and are mathematically described as a Dirac delta function lying along the immersed structure. In this paper we first review on various ways of modeling the elastic forces in different physical situations. Then we focus on the discretization of the immersed boundary method by means of finite elements which can handle the Dirac delta function variationally avoiding the introduction of its regularization. Practical computational aspects are described and some preliminary numerical experiment in two dimensions are reported.
Simulations of the whirling instability by the immersed boundary method
 SIAM J. Sci. Comput
, 2004
"... Abstract. When an elastic filament spins in a viscous incompressible fluid it may undergo a whirling instability, as studied asymptotically by Wolgemuth, Powers, and Goldstein [Phys. Rev. Lett., 84 (2000), pp. 16–23]. We use the immersed boundary (IB) method to study the interaction between the elas ..."
Abstract

Cited by 19 (4 self)
 Add to MetaCart
(Show Context)
Abstract. When an elastic filament spins in a viscous incompressible fluid it may undergo a whirling instability, as studied asymptotically by Wolgemuth, Powers, and Goldstein [Phys. Rev. Lett., 84 (2000), pp. 16–23]. We use the immersed boundary (IB) method to study the interaction between the elastic filament and the surrounding viscous fluid as governed by the incompressible Navier–Stokes equations. This allows the study of the whirling motion when the shape of the filament is very different from the unperturbed straight state.
SIMULATING THE FLUID DYNAMICS OF NATURAL AND PROSTHETIC HEART VALVES USING THE IMMERSED BOUNDARY METHOD
, 2009
"... The immersed boundary method is both a general mathematical framework and a particular numerical approach to problems of fluidstructure interaction. In the present work, we describe the application of the immersed boundary method to the simulation of the fluid dynamics of heart valves, including a ..."
Abstract

Cited by 19 (6 self)
 Add to MetaCart
The immersed boundary method is both a general mathematical framework and a particular numerical approach to problems of fluidstructure interaction. In the present work, we describe the application of the immersed boundary method to the simulation of the fluid dynamics of heart valves, including a model of a natural aortic valve and a model of a chorded prosthetic mitral valve. Each valve is mounted in a semirigid flow chamber. In the case of the mitral valve, the flow chamber is a circular pipe, and in the case of the aortic valve, the flow chamber is a model of the aortic root. The model valves and flow chambers are immersed in a viscous incompressible fluid, and realistic fluid boundary conditions are prescribed at the upstream and downstream ends of the chambers. To connect the immersed boundary models to the boundaries of the fluid domain, we introduce a novel modification of the standard immersed boundary scheme. In particular, near the outer boundaries of the fluid domain, we modify the construction of the regularized delta function which mediates fluidstructure coupling in the immersed boundary method, whereas in the interior of the fluid domain, we employ a standard fourpoint delta function which is frequently used with the immersed boundary method. The standard delta
LatticeBased Flow Field Modeling
 IEEE Transactions on Visualization and Computer Graphics
"... Abstract—We present an approach for simulating the natural dynamics that emerge from the interaction between a flow field and immersed objects. We model the flow field using the Lattice Boltzmann Model (LBM) with boundary conditions appropriate for moving objects and accelerate the computation on co ..."
Abstract

Cited by 18 (8 self)
 Add to MetaCart
(Show Context)
Abstract—We present an approach for simulating the natural dynamics that emerge from the interaction between a flow field and immersed objects. We model the flow field using the Lattice Boltzmann Model (LBM) with boundary conditions appropriate for moving objects and accelerate the computation on commodity graphics hardware (GPU) to achieve realtime performance. The boundary conditions mediate the exchange of momentum between the flow field and the moving objects resulting in forces exerted by the flow on the objects as well as the backcoupling on the flow. We demonstrate our approach using soap bubbles and a feather. The soap bubbles illustrate Fresnel reflection, reveal the dynamics of the unseen flow field in which they travel, and display spherical harmonics in their undulations. Our simulation allows the user to directly interact with the flow field to influence the dynamics in real time. The free feather flutters and gyrates in response to lift and drag forces created by its motion relative to the flow. Vortices are created as the free feather falls in an otherwise quiescent flow. Index Terms—Lattice Boltzmann model, force evaluation, flow field interaction, hardware acceleration, twoway solidfluid coupling, bubble simulation, feather simulation, computation on GPU.
BJ (2008) Vortex shedding model of a flapping flag
 J Fluid Mech
"... A twodimensional model for the flapping of an elastic flag under axial flow is described. The vortical wake is accounted for by the shedding of discrete point vortices with unsteady intensity, enforcing the regularity condition at the flag's trailing edge. The stability of the flat state of r ..."
Abstract

Cited by 17 (1 self)
 Add to MetaCart
A twodimensional model for the flapping of an elastic flag under axial flow is described. The vortical wake is accounted for by the shedding of discrete point vortices with unsteady intensity, enforcing the regularity condition at the flag's trailing edge. The stability of the flat state of rest as well as the characteristics of the flapping modes in the periodic regime are compared successfully to existing linear stability and experimental results. An analysis of the flapping regime shows the coexistence of direct kinematic waves, travelling along the flag in the same direction as the imposed flow, and reverse dynamic waves, travelling along the flag upstream from the trailing edge. Introduction A fluttering instability can develop from the interaction of the internal dynamics of an elastic structure and an axial flow. The flapping of windforced flags is a canonical example of such an interaction problem, which is also of interest in various other engineering The fluttering flag instability has been the focus of a large number of experimental studies including soapfilm To understand the onset of the instability, several papers have focused on the linear stability of the flat position. The twodimensional linear stability of infinite membranes under axial flow was first studied by Rayleigh (1878). More recently, The purpose of the present work is to propose a reducedorder model for the flow over the flag, able to obtain the longtime behaviour and finiteamplitude flapping. It also reproduces the main characteristics of the problem as observed in full numerical simulations and experiments while significantly reducing the computational complexity. A potential flow representation is used for the twodimensional flow past an infinitely thin inextensible elastic strip of finite length. The wake is represented by discrete point vortices, unlike the vortex sheet representation described in Model A twodimensional model of a flapping flag is considered. The flag is inextensible and clamped at its fixed end; L, B and ρ s are respectively its length, bending rigidity and mass per unit length. The surrounding fluid density is ρ, and a uniform horizontal flow at infinity U ∞ is prescribed. In the following, all quantities are nondimensionalized using L, U ∞ and ρ as reference values. Positions and velocities are defined with respect to a fixed system of axes with origin at the clamped end of the flag. Solid model A finitedisplacement inextensible EulerBernoulli beam model is considered. The position of the flag is ζ (s, t) (0 6 s 6 1 is the arclength), and θ(s, t) is the angle between the local tangent and the horizontal axis (see where a subscript s stands for ∂/∂s and dotted variables for ∂/∂t, with clampedfree boundary conditions: This model is equivalent to the one used in U * is the freestream velocity nondimensionalized by the flag rigidity and inertia. Vortex shedding model The flow around the flag is assumed to be irrotational. To satisfy the regularity condition for the flow at the trailing edge, point vortices are introduced following the method suggested by where the overbar denotes the complex conjugate. The second term accounts for the conservation of fluid momentum around the vortex and associated branch cut, and w n is the desingularized flow velocity at the vortex position (Saffman 1992). When a vortex reaches maximum intensity, the intensity of this vortex is frozen and a new vortex is started from the shedding corner. Because the angle of attack is always small in this problem, vortex shedding is neglected at the leading edge and vortices are shed from the trailing edge only. Therefore at any time, the vortex wake consists of N − 1 vortices (z j (t), Γ j ) with steady intensity and one unsteady point vortex (z N (t), Γ N (t)). Fluid model Using the Plemelj formula and following 2.4. Numerical method for the flag problem A system of equations for θ and T alone can be obtained by combining both equations in (2.1): (2.8b) Determining the flag position as ζ (s, t) = s 0 e iθ ds automatically satisfies the inextensibility condition. Then the boundary conditions are obtained from (2.2) and Newton's second law applied to the whole flag as Expanding θ as a superposition of Chebyshev polynomials θ = c j (t)T j (2s − 1), (2.4), (2.5), (2.7) and (2.8) are used to integrate c j and (z n ,Γ n ) in time using a secondorderaccurate finitedifference scheme. The fourthorder derivative in space in (2.8b) is treated semiimplicitely and all nonlinear terms in (2.8) are evaluated explicitely. Chebyshev spectral methods are particularly adapted to handle the squareroot singular behaviour of the general solution of (2.5a) near s = 0 and s = 1. From (2.4), (2.6) and the time derivative of (2.5),Γ N ,ż n ,κ and therefore [p] ± depend onθ linearly. In (2.8), the contribution of the solid acceleration to the pressure (added inertia) can be isolated to computec j directly, thereby greatly reducing the computational cost in comparison with other methods which require an iterative solver at each timestep of the fluidsolid problem (Alben & Shelley 2008). The secondorder accuracy of the solver was checked using (2.1) and the conservation of Results The flag is initially at rest (θ(s, t < 0) = 0) and at t = 0 the horizontal flow at infinity is ramped up continuously to its longtime value. A small transient vertical perturbation is added to perturb this trivial equilibrium (of the form v = t p e −qt ; different values of p and q were tested with no significant impact on the longtime behaviour). In each run, the rigidity and inertia of the flag are fixed, and the flow at infinity can be varied inducing a change of the nondimensional velocity U * defined in (2.3). 3.1. Three possible regimes For a given inertia ratio M * , three regimes were observed. For small U * (low wind speed), the initial perturbation creates a small motion of the flag that quickly decays, and the flag returns to its rest position. When U * is increased above a critical value U * c (U * c = 9.6 for M * = 3), this rest position becomes unstable. For intermediate values of U * (9.6 6 U * 6 12 for M * = 3), a periodic flapping develops after a transient regime, in which the energy of the flag oscillates with an exponentially growing envelope. One point vortex is shed during each halfstroke and the intensity of the point vortices have alternating signs. Downstream from the flag (about one flag length), these point vortices arrange in a weak von Kármán street and are advected with U ∞ close to the horizontal axis (figure 2). This is in good agreement with the positioning of the centres of vorticity in the vortex sheet approach The motion of the flag in this flapping regime is highly periodic. The power spectra of the flag total energy (2.10) and tail orientation θ(1, t) display sharp peaks (see the lefthand column of Comparison with linear stability results For a given M * , the critical velocity U * c above which the rest state of the flag becomes unstable is computed. The corresponding critical curve is plotted in figure 4 in both the (M * , U * ) and (µ, η) planes for comparison with previous studies. We also plot for reference the results from the linear stability analysis Hysteresis behaviour Experimental studies on flapping flags have pointed out the hysteresis behaviour of the flag when the velocity of the flow at infinity is varied
Systematic derivation of jump conditions for the immersed interface method in threedimensional flow simulation
 SIAM J. Sci. Comput
"... Abstract. In this paper, we systematically derive jump conditions for the immersed interface ..."
Abstract

Cited by 12 (3 self)
 Add to MetaCart
Abstract. In this paper, we systematically derive jump conditions for the immersed interface