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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 ..."
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Cited by 19 (6 self)
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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
On the Volume Conservation of the Immersed Boundary Method
, 2012
"... Abstract. The immersed boundary (IB) method is an approach to problems of fluidstructure interaction in which an elastic structure is immersed in a viscous incompressible fluid. The IB formulation of such problems uses a Lagrangian description of the structure and an Eulerian description of the f ..."
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Abstract. The immersed boundary (IB) method is an approach to problems of fluidstructure interaction in which an elastic structure is immersed in a viscous incompressible fluid. The IB formulation of such problems uses a Lagrangian description of the structure and an Eulerian description of the fluid. It is well known that some versions of the IB method can suffer from poor volume conservation. Methods have been introduced to improve the volumeconservation properties of the IB method, but they either have been fairly specialized, or have used complex, nonstandard Eulerian finitedifference discretizations. In this paper, we use quasistatic and dynamic benchmark problems to investigate the effect of the choice of Eulerian discretization on the volumeconservation properties of a formally secondorder accurate IB method. We consider both collocated and staggeredgrid discretization methods. For the tests considered herein, the staggeredgrid IB scheme generally yields at least a modest improvement in volume conservation when compared to cellcentered methods, and in many cases considered in this work, the spurious volume changes exhibited by the staggeredgrid IB method are more than an order of magnitude smaller than those of
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 ..."
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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.
1 Parallel EulerianLagrangian Method with Adaptive Mesh Refinement for Moving Boundary Computation
"... In this study, we present a parallelized adaptive moving boundary computation technique on distributed memory multiprocessor systems for multiscale multiphase flow simulations. The solver utilizes the EulerianLagrangian method to track moving (Lagrangian) interfaces explicitly on the stationary ( ..."
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Cited by 1 (1 self)
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In this study, we present a parallelized adaptive moving boundary computation technique on distributed memory multiprocessor systems for multiscale multiphase flow simulations. The solver utilizes the EulerianLagrangian method to track moving (Lagrangian) interfaces explicitly on the stationary (Eulerian) Cartesian grid where the flow fields are computed. Since there exists strong data and task dependency between two distinct Eulerian and Lagrangian domain, we address the decomposition strategies for each domain separately. We then propose a tradeoff approach aiming for parallel scalability. Spatial domain decomposition is adopted for both Eulerian and Lagrangian domains for load balancing and data locality to minimize interprocessor communication. In addition, a cellbased unstructured parallel adaptive mesh refinement (AMR) technique is implemented for the flexible local refinement with efficient grid usage and evendistributed computational workload among processors. The parallel performance is evaluated independently for the Cartesian grid solver and subprocedures in cellbased unstructured AMR. The capability and the overall performance of the parallel adaptive EulerianLagrangian method including moving boundary and topological change is demonstrated by modeling binary droplet collisions. With the aid of the present techniques, large scale moving boundary problems can be effectively computed. 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 ..."
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doi:10.1093/imamat/hxu029 Dynamic finitestrain modelling of the human left ventricle in health and disease using an immersed boundaryfinite element method
unknown title
, 2013
"... Parallel processing of EulerianLagrangian, cellbased adaptive method for moving boundary problems by ..."
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Parallel processing of EulerianLagrangian, cellbased adaptive method for moving boundary problems by
Simulating an Elastic Ring with Bend and Twist by anAdaptiveGeneralized Immersed BoundaryMethod
, 2011
"... Abstract. Many problems involving the interaction of an elastic structure and a viscous fluid can be solved by the immersed boundary (IB) method. In the IB approach to such problems, the elastic forces generated by the immersed structure are applied to the surrounding fluid, and the motion of the i ..."
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Abstract. Many problems involving the interaction of an elastic structure and a viscous fluid can be solved by the immersed boundary (IB) method. In the IB approach to such problems, the elastic forces generated by the immersed structure are applied to the surrounding fluid, and the motion of the immersed structure is determined by the local motion of the fluid. Recently, the IB method has been extended to treat more general elasticity models that include both positional and rotational degrees of freedom. For such models, force and torque must both be applied to the fluid. The positional degrees of freedom of the immersed structure move according to the local linear velocity of the fluid, whereas the rotational degrees of freedommove according to the local angular velocity. This paper introduces a spatially adaptive, formally secondorder accurate version of this generalized immersed boundary method. We use this adaptive scheme to simulate the dynamics of an elastic ring immersed in fluid. To describe the elasticity of the ring, we use an unconstrained version of Kirchhoff rod theory. We demonstrate empirically that our numerical scheme yields essentially secondorder convergence rates when applied to such problems. We also study dynamical instabilities of such fluidstructure systems, and we compare numerical results produced by our method to classical analytic results from elastic rod theory.