Results 1  10
of
22
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
STOCHASTIC EULERIAN LAGRANGIAN METHODS FOR FLUIDSTRUCTURE INTERACTIONS WITH THERMAL FLUCTUATIONS
, 2010
"... Abstract. We present approaches for the study of fluidstructure interactions subject to thermal fluctuations. A mixed mechanical description is utilized combining Eulerian and Lagrangian reference frames. We establish general conditions for operators coupling these descriptions. Stochastic driving ..."
Abstract

Cited by 10 (1 self)
 Add to MetaCart
(Show Context)
Abstract. We present approaches for the study of fluidstructure interactions subject to thermal fluctuations. A mixed mechanical description is utilized combining Eulerian and Lagrangian reference frames. We establish general conditions for operators coupling these descriptions. Stochastic driving fields for the formalism are derived using principles from statistical mechanics. The stochastic differential equations of the formalism are found to exhibit significant stiffness in some physical regimes. To cope with this issue, we derive reduced stochastic differential equations for several physical regimes. We also present stochastic numerical methods for each regime to approximate the fluidstructure dynamics and to generate efficiently the required stochastic driving fields. To validate the methodology in each regime, we perform analysis of the invariant probability distribution of the stochastic dynamics of the fluidstructure formalism. We compare this analysis with results from statistical mechanics. To further demonstrate the applicability of the methodology, we perform computational studies for spherical particles having translational and rotational degrees of freedom. We compare these studies with results from fluid mechanics. The presented approach provides for fluidstructure systems a set of rather general computational methods for treating consistently structure mechanics, hydrodynamic coupling, and thermal fluctuations.
Numerical simulations of twodimensional foam by the immersed boundary method
 J. of Comput. Phys
"... In this paper, we present an immersed boundary (IB) method to simulate a dry foam, i.e., a foam in which most of the volume is attributed to its gas phase. Dry foam dynamics involves the interaction between a gas and a collection of thin liquidfilm internal boundaries that partition the gas into dis ..."
Abstract

Cited by 6 (1 self)
 Add to MetaCart
(Show Context)
In this paper, we present an immersed boundary (IB) method to simulate a dry foam, i.e., a foam in which most of the volume is attributed to its gas phase. Dry foam dynamics involves the interaction between a gas and a collection of thin liquidfilm internal boundaries that partition the gas into discrete cells or bubbles. The liquid film boundaries are flexible, contract under the influence of surface tension, and are permeable to the gas, which moves across them by diffusion at a rate proportional to the local pressure difference across the boundary. Such problems are conventionally studied by assuming that the pressure is uniform within each bubble. Here, we introduce instead an IB method that takes into account the nonequilibrium fluid mechanics of the gas. To model gas diffusion across the internal liquidfilm boundaries, we allow normal slip between the boundary and the gas at a velocity proportional to the (normal) force generated by the boundary surface tension. We implement this method in the twodimensional case, and test it by verifying the vonNeumann relation, which governs the coarsening of a twodimensional dry foam. The method is further validated by a convergence study, which confirms its firstorder accuracy.
A Multirate Time Integrator for Regularized Stokeslets
"... The method of regularized Stokeslets is a numerical approach to approximating solutions of fluidstructure interaction problems in the Stokes regime. Regularized Stokeslets are fundamental solutions to the Stokes equations with a regularized pointforce term that are used to represent forces generat ..."
Abstract

Cited by 6 (1 self)
 Add to MetaCart
(Show Context)
The method of regularized Stokeslets is a numerical approach to approximating solutions of fluidstructure interaction problems in the Stokes regime. Regularized Stokeslets are fundamental solutions to the Stokes equations with a regularized pointforce term that are used to represent forces generated by rigid or elastic object interacting with the fluid. Due to the linearity of the Stokes equations, the velocity at any point in the fluid can be computed by summing the contributions of regularized Stokeslets, and the time evolution of positions can be computed using standard methods for ordinary differential equations. Rigid or elastic objects in the flow are usually treated as immersed boundaries represented by a collection of regularized Stokeslets coupled together by virtual springs which determine the forces exerted by the boundary in the fluid. For problems with boundaries modeled by springs with large spring constants, the resulting ordinary differential equations become stiff, and hence the time step for explicit time integration methods is severely constrained. Unfortunately, the
STOCHASTIC REDUCTIONS FOR INERTIAL FLUIDSTRUCTURE INTERACTIONS SUBJECT TO THERMAL FLUCTUATIONS
"... Abstract. We investigate the dynamics of elastic microstructures that interact with a fluid flow when subject to thermal fluctuations. We perform analysis to obtain systematically simplified descriptions of the mechanics in the limiting regimes when (i) the coupling forces that transfer momentum bet ..."
Abstract

Cited by 4 (1 self)
 Add to MetaCart
(Show Context)
Abstract. We investigate the dynamics of elastic microstructures that interact with a fluid flow when subject to thermal fluctuations. We perform analysis to obtain systematically simplified descriptions of the mechanics in the limiting regimes when (i) the coupling forces that transfer momentum between the fluid and microstructures is strong, (ii) the mass of the microstructures is small relative to the displaced mass of the fluid, and (iii) the response to stresses results in hydrodynamics that relax rapidly to a quasisteadystate relative to the motions of the microstructure. We derive effective equations using a singular perturbation analysis of the Backward Kolmogorov equations of the stochastic process. Our continuum mechanics description is based on the Stochastic Eulerian Lagrangian Method (SELM) which provides a framework for approximation of the fluidstructure interactions when subject to thermal fluctuations. We perform a dimension analysis of the SELM equations to identify key nondimensional groups and to characterize precisely each of the limiting physical regimes. The reduced equations offer insights into the physical accuracy of SELM descriptions in comparison with classical results. The reduced equations also elimintate rapid timescales from the dynamics and provide possible approaches for the development of more efficient computational methods for simulations of fluidstructure interactions when subject to thermal fluctuations.
Simulating cardiovascular fluid dynamics by the immersed boundary method
 in 47th AIAA Aerospace Sciences Meeting
, 2009
"... The immersed boundary method is both a general mathematical framework and a particular numerical approach to problems of fluidstructure interaction. In this paper, we describe the application of the immersed boundary method to the simulation of cardiovascular fluid dynamics, focusing on the fluid ..."
Abstract

Cited by 1 (0 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 this paper, we describe the application of the immersed boundary method to the simulation of cardiovascular fluid dynamics, focusing on the fluid dynamics of the aortic heart valve (the valve which prevents the backflow of blood from the aorta into the left ventricle of the heart) and aortic root (the initial portion of the aorta, which attaches to the heart). The aortic valve and root are modeled as a system of elastic fibers, and the blood is modeled as a viscous incompressible fluid. Threedimensional simulation results obtained using a parallel and adaptive version of the immersed boundary method are presented. These results demonstrate that it is feasible to perform threedimensional immersed boundary simulations of cardiovascular fluid dynamics in which realistic cardiac output is obtained at realistic pressures. Nomenclature U physical domain x = (x, y, z) ∈ U Cartesian (physical) coordinates u(x, t) fluid velocity p(x, t) fluid pressure f(x, t) Eulerian force density applied by the structure to the fluid δ(x) = δ(x) δ(y) δ(z) threedimensional Dirac delta function δh(x) = δh(x) δh(y) δh(z) threedimensional regularized Dirac delta function Ω Lagrangian coordinate domain (q, r, s) ∈ Ω Lagrangian (material) coordinates X(q, r, s, t) physical position of Lagrangian (material) point (q, r, s) at time t F(q, r, s, t) Lagrangian force density applied by the structure to the fluid I.
unknown title
, 2014
"... doi:10.1093/imamat/hxu029 Dynamic finitestrain modelling of the human left ventricle in health and disease using an immersed boundaryfinite element method ..."
Abstract
 Add to MetaCart
(Show Context)
doi:10.1093/imamat/hxu029 Dynamic finitestrain modelling of the human left ventricle in health and disease using an immersed boundaryfinite element method
Numerical Study of Stability and Accuracy of the Immersed Boundary Method Coupled to the Lattice Boltzmann BGKModel
, 2014
"... Abstract. This paper aims to study the numerical features of a coupling scheme between the immersed boundary (IB) method and the lattice Boltzmann BGK (LBGK) model by four typical test problems: the relaxation of a circular membrane, the shearing flow induced by a moving fiber in the middle of a c ..."
Abstract
 Add to MetaCart
(Show Context)
Abstract. This paper aims to study the numerical features of a coupling scheme between the immersed boundary (IB) method and the lattice Boltzmann BGK (LBGK) model by four typical test problems: the relaxation of a circular membrane, the shearing flow induced by a moving fiber in the middle of a channel, the shearing flow near a nonslip rigid wall, and the circular Couette flow between two inversely rotating cylinders. The accuracy and robustness of the IBLBGK coupling scheme, the performances of different discrete Dirac delta functions, the effect of iteration on the coupling scheme, the importance of the external forcing term treatment, the sensitivity of the coupling scheme to flow and boundary parameters, the velocity slip near nonslip rigid wall, and the origination of numerical instabilities are investigated in detail via the four test cases. It is found that the iteration in the coupling cycle can effectively improve stability, the introduction of a secondorder forcing term in LBGK model is crucial, the discrete fiber segment length and the orientation of the fiber boundary obviously affect accuracy and stability, and the emergence of both temporal and spatial fluctuations of boundary parameters seems to be the indication of numerical instabil
SIMULATING FLEXIBLE FIBER SUSPENSIONS USING A SCALABLE IMMERSED BOUNDARY ALGORITHM
"... We present an approach for numerically simulating the dynamics of flexible fibers in a threedimensional shear flow using a scalable immersed boundary (IB) algorithm based on Guermond and Minev’s pseudocompressible fluid solver. The fibers are treated as onedimensional Kirchhoff rods that resist ..."
Abstract
 Add to MetaCart
We present an approach for numerically simulating the dynamics of flexible fibers in a threedimensional shear flow using a scalable immersed boundary (IB) algorithm based on Guermond and Minev’s pseudocompressible fluid solver. The fibers are treated as onedimensional Kirchhoff rods that resist stretching, bending, and twisting, within the generalized IB framework. We perform a careful numerical comparison against experiments on single fibers performed by S. G. Mason and coworkers, who categorized the fiber dynamics into several distinct orbit classes. We show that the orbit class may be determined using a single dimensionless parameter for low Reynolds flows. Lastly, we simulate dilute suspensions containing up to hundreds of fibers using a distributedmemory computer cluster. These simulations serve as a stepping stone for studying more complex suspension dynamics including nondilute suspensions and aggregation of fibers (also known as flocculation).