Results

**11 - 19**of**19**### SIMULATING FLEXIBLE FIBER SUSPENSIONS USING A SCALABLE IMMERSED BOUNDARY ALGORITHM

"... We present an approach for numerically simulating the dynamics of flexible fibers in a three-dimensional shear flow using a scalable immersed boundary (IB) algorithm based on Guermond and Minev’s pseudo-compressible fluid solver. The fibers are treated as one-dimensional Kirchhoff rods that resist ..."

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We present an approach for numerically simulating the dynamics of flexible fibers in a three-dimensional shear flow using a scalable immersed boundary (IB) algorithm based on Guermond and Minev’s pseudo-compressible fluid solver. The fibers are treated as one-dimensional 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 co-workers, 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 distributed-memory computer cluster. These simulations serve as a stepping stone for studying more complex suspension dynamics including non-dilute suspensions and aggregation of fibers (also known as flocculation).

### INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING

"... On hypersingular surface integrals in the symmetric Galerkin boundary element method: application to heat conduction in exponentially graded materials ..."

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On hypersingular surface integrals in the symmetric Galerkin boundary element method: application to heat conduction in exponentially graded materials

### unknown title

, 2008

"... equations using the projection method as a preconditioner a r t i c l e i n f o incompressible flow problems which obtains updated values for the fluid velocity u and pressure p in two steps. First, an approximation to the momentum equation is solved over a time interval Dt without imposing the cons ..."

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equations using the projection method as a preconditioner a r t i c l e i n f o incompressible flow problems which obtains updated values for the fluid velocity u and pressure p in two steps. First, an approximation to the momentum equation is solved over a time interval Dt without imposing the constraint of incompress-ibility, yielding an ‘‘intermediate ” fluid velocity field u, and generallyr u – 0. To obtain an approximation to the updated fluid velocity which does satisfy the constraint of incompressibility, the projection method uses the Hodge decomposition to compute efficiently the projection of u onto the space of divergence-free vector fields. Doing so requires the solution of a 0021-9991/ $- see front matter 2009 Elsevier Inc. All rights reserved.

### 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 vis-cous 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 vis-cous 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 gen-eral 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 veloc-ity of the fluid, whereas the rotational degrees of freedommove according to the local angular velocity. This paper introduces a spatially adaptive, formally second-order ac-curate 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 second-order convergence rates when applied to such problems. We also study dynamical instabil-ities of such fluid-structure systems, and we compare numerical results produced by our method to classical analytic results from elastic rod theory.

### Dedication

, 2015

"... iii Acknowledgments I’d like to acknowledge my advisor, Dr. Aleksandar Donev, for being an exceptional mentor. Without his guidance, dedication, and patience, this work would have never been possible. I also must express my deep appreciation for the collaboration of Dr. Eric Vanden-Eijnden, who cont ..."

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iii Acknowledgments I’d like to acknowledge my advisor, Dr. Aleksandar Donev, for being an exceptional mentor. Without his guidance, dedication, and patience, this work would have never been possible. I also must express my deep appreciation for the collaboration of Dr. Eric Vanden-Eijnden, who contributed significantly to the work done in this thesis. I’d also like to thank the rest of my committee, Dr. Miranda Holmes-Cerfon, Dr. Jonathan Goodman, and Dr. Charles Peskin for taking the time to review my work and provide insightful comments. I extend my sincere thanks to Dr. Boyce Griffith for providing help in using the IBAMR software framework, which proved indispensable for the implementation of many of the methods introduced in this work. I am very grateful to my colleagues Dr. Florencia Balboa and Yifei Sun for their hard work on this project and for running several numerical tests to validate our methods. Additionally, I’d like to thank my fellow students at the Courant Institute, for always being available to discuss the issues in my research and for providing a sense of friendship and community that made my time as a graduate student very enjoyable. This research would not have been possible without funding from the NSF under award OCI 1047734 and from

### A Modular, Operator Splitting Scheme for Fluid-Structure Interaction Problems with Thick Structures

, 2013

"... We present an operator-splitting scheme for fluid-structure interaction (FSI) problems in hemodynamics, where the thickness of the structural wall is com-parable to the radius of the cylindrical fluid domain. The equations of linear elasticity are used to model the structure, while the Navier-Stokes ..."

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We present an operator-splitting scheme for fluid-structure interaction (FSI) problems in hemodynamics, where the thickness of the structural wall is com-parable to the radius of the cylindrical fluid domain. The equations of linear elasticity are used to model the structure, while the Navier-Stokes equations for an incompressible viscous fluid are used to model the fluid. The operator splitting scheme, based on Lie splitting, separates the elastodynamics struc-ture problem, from a fluid problem in which structure inertia is included to achieve unconditional stability. We prove energy estimates associated with unconditional stability of this modular scheme for the full nonlinear FSI prob-lem defined on a moving domain, without requiring any sub-iterations within time steps. Two numerical examples are presented, showing excellent agree-ment with the results of monolithic schemes. First-order convergence in time is shown numerically. Modularity, unconditional stability without temporal sub-iterations, and simple implementation are the features that make this operator-splitting scheme particularly appealing for multi-physics problems involving fluid-structure interaction.

### Augmenting the Immersed Boundary Method with Radial Basis Functions (RBFs) for the Modeling of Platelets in Hemodynamic Flows

, 2014

"... ar ..."

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### IMMERSED BOUNDARY METHOD FOR SHARED-MEMORY ARCHITECTURES

"... Abstract. In this report, we propose a novel, massively parallelizable algorithm for the immersed boundary method based on the fluid solver of Guermond and Minev [11]. This solver employs a directional-splitting technique that allows the incompressible Navier–Stokes equation to be efficiently parall ..."

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Abstract. In this report, we propose a novel, massively parallelizable algorithm for the immersed boundary method based on the fluid solver of Guermond and Minev [11]. This solver employs a directional-splitting technique that allows the incompressible Navier–Stokes equation to be efficiently parallelized on both shared and distributed memory architectures. An implementation of the numerical scheme was constructed in Python and C/C++, where the bottlenecks were parallelized using OpenMP. The parallelization techniques used in our implementation are discussed. Furthermore, results for a fluid-structure interaction problem are shown along with a corresponding performance study. 1.

### physiological driving and loading conditions

"... Immersed boundary model of aortic heart valve dynamics with ..."

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