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## A massively parallel adaptive sharp interface solver with application to mechanical heart valve simulations (2012)

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### Citations

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Citation Context ... thescloud. ................................................................................................................53sFigure 11sThe 16 standard configurations of the Marching Cubes algorithm =-=[74]-=-.sThe intersection of an isocontour with the edges of a computational cellsleads to arbitrary polygonal shapes. Marching cubes efficientlysdetermines the shape from a hexadecimal lookup table using th... |

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Iterative Methods for Sparse Linear Systems
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Citation Context ... steps of the fractional step algorithm. Effective preconditioning can dramaticallysincrease convergence by shifting and clustering the eigenvalues of the linear problemsaway from the zero eigenvalue =-=[87]-=-. Of particular importance is the construction of ansefficient preconditioning technique for the Poisson equation contained in the fractionalsstep algorithm, which accounts for almost 90% of the flow ... |

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Using MPI: Portable Parallel Programming with the Message–Passing Interface
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Citation Context ... current implementation, the computational grid is a completely distributedsCartesian base mesh which is enriched with local refinement and mesh pruning. Thesmesh is partitioned using the MPI library =-=[75]-=- such that no MPI process contains a copysof any globally sized mesh entity. Local refinement is achieved using a forest of octreessapproach [28]. Each base mesh cell holds the root of a fully-threade... |

701 | Level Set Methods and Fast Marching Methods. Evolving Interfaces
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Citation Context ... formation in mechanical heart valves. An efficientsmoving boundary flow solver can be based on a Cartesian grid interface treatmentsapproach [26] combined with level set representation of geometries =-=[27]-=-. There existsmesh refinement algorithms for Cartesian grids which scale on the largestssupercomputers currently available and which can be used to increase the efficiency ofsthe method [28, 29]. This... |

528 |
Computational Methods for Fluid Dynamics
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Citation Context ...cessful insthese applications, extending the methodology to boundaries with large scale boundarysmotion may be difficult to manage due to the complexity of generating high qualitysunstructured meshes =-=[23]-=-. In [24], patient specific cardiovascular geometries weresobtained from medical images and the flow fields were subsequently computed using ansunstructured Cartesian approach with a reduced memory fo... |

519 |
Local adaptive mesh refinement for shock hydrodynamics
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Citation Context ...tored on leaf cells.sThe use of adaptive meshing of Cartesian grids is an established concept. ThesAdaptive Mesh Refinement (AMR) approach refine a grid in a nested set of regularsrectangular patches =-=[76, 77]-=-. AMR libraries such as PARAMESH [78] and SAMRAI [29]s63shave been developed to remove the burden of mesh management from applicationsprogrammers. The use of octree-based refinement has also been used... |

421 | A fast level set method for propagating interfaces
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Citation Context ...-order WENO upwindsspatial discretizations [64, 65]. In order to save computational effort and memory, theslevel set is only calculated and stored in a narrow band of grid points around the interfaces=-=[66]-=-, or more specifically a dynamic tubular grid [67]. As the level set moves, the narrowsband requires rebuilding so the zero level set contour does not pass out of the domainsover which it is computed.... |

374 |
The immersed boundary method
- Peskin
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Citation Context ...xterior of the object. Any particular continuous forcing method issdefined by the form of the forcing term, f⃗b. The most popular continuous forcing methodshas been the Immersed Boundary Method (IBM) =-=[31, 32]-=- which was developed tosfacilitate the solution of the flow of blood in the human heart [33]. In this approach,ssingular surface forces defined on a Lagrangian mesh are converted to volumetric forcess... |

331 |
Numerical analysis of blood flow in the heart
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Citation Context ...rcing term, f⃗b. The most popular continuous forcing methodshas been the Immersed Boundary Method (IBM) [31, 32] which was developed tosfacilitate the solution of the flow of blood in the human heart =-=[33]-=-. In this approach,ssingular surface forces defined on a Lagrangian mesh are converted to volumetric forcessdefined on Cartesian flow mesh using numerical delta functions. This approach has foundsexte... |

321 | A non-oscillatory Eulerian approach to interfaces in multimaterial flows (the Ghost Fluid Method
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Citation Context ...lso generally slightlysless accurate than the other approaches. In this work, we adopt the ghost fluid approachsdue to its simplicity.sThe concept of a ghost fluid, first popularized by Fedkiw et al. =-=[48]-=-, wassoriginally used to simulate shocks and discontinuities. The approach was extended to thessolution of Poisson and heat equations by Gibou et al. in [49] and later a fourth-ordersGFM scheme based ... |

273 | The immersed interface method for elliptic equations with discontinuous coefficients and singular sources
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Citation Context ...ing cells [35-37]. However, IBM has several drawbacks. First, thesnumerical delta function spreads the force over a finite support which smears the effect ofsthe interface, thereby degrading accuracy =-=[38]-=-. Additionally, the above approach requiressspecial treatment to handle rigid boundaries [39]. Improvements have been made to thesIBM in recent years [39, 40], and the idea of transmitting the effect ... |

239 |
Fully multidimensional flux-corrected transport algorithms for fluids
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Citation Context ...er period of deformation.s4.3 The Zalesak Disk ProblemsIn the current section, the behavior of the current level set technique near sharpsedges is investigated by solving for the Zalesak disk problem =-=[91]-=-. The disk of radius 0.2sis originally centered at (0.5,0.75) in a 1x1 domain. The disk is then rotated once aboutsthe point (0.5,0.5) with a rigid body velocity ofs... |

226 | Weighted ENO schemes for Hamilton–Jacobi equations
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(Show Context)
Citation Context ...severywhere else.sThe level set advection equation (2.3) is solved numerically using a 3rd-ordersTVD Runge-Kutta time-stepping scheme in conjunction with 5th-order WENO upwindsspatial discretizations =-=[64, 65]-=-. In order to save computational effort and memory, theslevel set is only calculated and stored in a narrow band of grid points around the interfaces[66], or more specifically a dynamic tubular grid [... |

211 |
Heart disease and stroke statistics—2009 update: a report from the American Heart Association Statistics Committee and Stroke Statistics Subcommittee. Circulation
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Citation Context ...nsA common treatment for compromised heart valves is surgical replacement withssome form of prosthetic valve, with approximately 100,000 replacement proceduressperformed in the United States annually =-=[1]-=-. Valve prostheses are generalized into twosbroad categories, mechanical heart valves (MHV) and bio-prosthetic heart valves (BHV).sThe most commonly used mechanical valves, accounting for 80% of mecha... |

158 |
Immersed boundary methods
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Citation Context ...nal components requiredsto examine the process of thrombus formation in mechanical heart valves. An efficientsmoving boundary flow solver can be based on a Cartesian grid interface treatmentsapproach =-=[26]-=- combined with level set representation of geometries [27]. There existsmesh refinement algorithms for Cartesian grids which scale on the largestssupercomputers currently available and which can be us... |

152 | Flow patterns around heart valves: a numerical method - Peskin - 1972 |

130 | A distributed Lagrange multiplier/fictitious domain method for particulate flows.
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Citation Context ...M in recent years [39, 40], and the idea of transmitting the effect of boundaries to thesfluid through the use of source has been extended to the finite element method by thesFictitious Domain Method =-=[41]-=- and Immersed Finite-Element Method [42].sRecently, many methods have moved away from using delta functions tosdistribute the force between grids. Instead, a forcing is derived in terms of the numeric... |

129 | Accurate projection methods for the incompressible navier-stokes equations
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- 2001
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Citation Context ...relate ϕ to pressure. It should besemphasized that ϕ is not pressure, but is instead a purely mathematical variable that cansbe related to pressure only when the discretization scheme has been chosen =-=[71]-=-. FromsEquation (2.10), it is clear that the boundary condition for equation (2.10) must be:s∂φ ∂n |∂Ω = (u�⃗∗∗−u�⃗n+1)∙n�⃗∆t |∂Ωs(2.11)sIf one sets the boundary condition for the intermediate velocit... |

119 | Combined immersedboundary finite-difference methods for three-dimensional complex flow simulations - Fadlun, Verzicco, et al. |

108 | An immersed boundary method with formal second-order accuracy and reduced numerical viscosity
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Citation Context ...reads the force over a finite support which smears the effect ofsthe interface, thereby degrading accuracy [38]. Additionally, the above approach requiressspecial treatment to handle rigid boundaries =-=[39]-=-. Improvements have been made to thesIBM in recent years [39, 40], and the idea of transmitting the effect of boundaries to thesfluid through the use of source has been extended to the finite element ... |

99 | Gerris: A tree-based adaptive solver for the incompressible Euler equations in complex geometries
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Citation Context ...ove the burden of mesh management from applicationsprogrammers. The use of octree-based refinement has also been used by manysresearchers. This approach forms the foundation of the GERRIS flow solver =-=[79]-=- andsp4est libraries [28]. The concept of pruning of a Cartesian grid is similar to the DynamicsTubular Grid (DTG) approach which was proposed by Nielsen and Museth [67] as asmore memory efficient alt... |

88 |
An adaptive version of the immersed boundary method
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- 1999
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Citation Context ... ofsthe interface, thereby degrading accuracy [38]. Additionally, the above approach requiressspecial treatment to handle rigid boundaries [39]. Improvements have been made to thesIBM in recent years =-=[39, 40]-=-, and the idea of transmitting the effect of boundaries to thesfluid through the use of source has been extended to the finite element method by thesFictitious Domain Method [41] and Immersed Finite-E... |

87 |
PARAMESH: A parallel adaptive mesh refinement community toolkit.”
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Citation Context ...meshing of Cartesian grids is an established concept. ThesAdaptive Mesh Refinement (AMR) approach refine a grid in a nested set of regularsrectangular patches [76, 77]. AMR libraries such as PARAMESH =-=[78]-=- and SAMRAI [29]s63shave been developed to remove the burden of mesh management from applicationsprogrammers. The use of octree-based refinement has also been used by manysresearchers. This approach f... |

83 | An efficient, interface-preserving level set redistancing algorithm and its application to interfacial incompressible fluid flow
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Citation Context ...tour does not pass out of the domainsover which it is computed. During this rebuilding step, points that are newly introducedsto the band are initialized with the level set re-initialization equation =-=[68]-=-:s∂ϕ ∂τ + sign(ϕ)n�⃗ ∙ ∇ϕ = 0s(2.4)sHere, τ is a pseudo-time, and the solution of equation (2.4) is marched to a steady state.sAfter convergence, the level set field satisfies the normal distance prop... |

82 | The immersed interface method for the navier stokes equations with singular forces
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Citation Context ...rs are constructed in a way such that boundarysconditions are directly incorporated into non-uniform discretization stencils. Examples ofsthis type of approach are the Immersed Interface Method (IIM) =-=[38, 46, 47]-=-, the GhostsFluid Method (GFM) [25, 48-50], the Sharp Interface Method (SIM) [51-53], and thesExtended Finite-Element Method (XFEM) [54-56]. The Immersed Interface Methodsconverts to normal and tangen... |

75 | A second order accurate symmetric discretization of the poisson equation on irregular domains
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Citation Context ... fluid, first popularized by Fedkiw et al. [48], wassoriginally used to simulate shocks and discontinuities. The approach was extended to thessolution of Poisson and heat equations by Gibou et al. in =-=[49]-=- and later a fourth-ordersGFM scheme based on dimension-by-dimension Lagrange interpolation was proposed ins[60]. The concept of a ghost fluid was extended to incompressible flows by Tseng ands17sFerz... |

75 | Adaptive Mesh Refinement using Wave-Propagation Algorithms for Hyperbolic Systems
- Berger, LeVeque
- 1998
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Citation Context ...tored on leaf cells.sThe use of adaptive meshing of Cartesian grids is an established concept. ThesAdaptive Mesh Refinement (AMR) approach refine a grid in a nested set of regularsrectangular patches =-=[76, 77]-=-. AMR libraries such as PARAMESH [78] and SAMRAI [29]s63shave been developed to remove the burden of mesh management from applicationsprogrammers. The use of octree-based refinement has also been used... |

74 |
An immersed-boundary finite-volume method for simulations of flow in complex geometries
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Citation Context ...e the pressuresoscillation does not significantly affect the velocity field, it can be problematic if thesmotion of a solid object is determined by the force induced by the pressure field. Kim etsal. =-=[44]-=- significantly reduced the pressure oscillation associated with their discrete forcingsapproach by utilizing mass sources/sinks to satisfy mass conservation at grid cells thatscontained the immersed i... |

73 |
Flow past a sphere up to a Reynolds number of 300
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Citation Context ...mmetric nature of the sphere, the wake is unsteadysand fully three-dimensional in the most general case. A steady axisymmetric wake issdeveloped for Reynolds number values less than approximately 210 =-=[93]-=-. For Reynoldssnumber values between 210 and 270, the wake settles into a non-symmetric steadyspattern, while Reynolds numbers above 270 display unsteady flow patterns. The richsstructures of the wake... |

72 | Spatially adaptive techniques for level set methods and incompressible flow, Comput. Fluids 35
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Citation Context ...severywhere else.sThe level set advection equation (2.3) is solved numerically using a 3rd-ordersTVD Runge-Kutta time-stepping scheme in conjunction with 5th-order WENO upwindsspatial discretizations =-=[64, 65]-=-. In order to save computational effort and memory, theslevel set is only calculated and stored in a narrow band of grid points around the interfaces[66], or more specifically a dynamic tubular grid [... |

70 |
High resolution simulations of the flow around and impulsively started cylinder using vortex methods
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Citation Context ...iscretizationsfor the solution of the level set advection equation. ......................................127sxiisFigure 39sA comparison the current results for vorticity contours with the resultssof =-=[92]-=- for an impulsively started flow around a stationary cylinder atsRe = 1000 at a time of 1, 2,s3, 4, 5, and 6. ....................................................128sFigure 40sA comparison of the curr... |

66 | A sharp interface Cartesian grid method for simulating flows with complex moving boundaries - Udaykumar, Mittal, et al. - 2001 |

55 |
A ghost-cell immersed boundary method for flow in complex geometry
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Citation Context ...was independent of the nature of the Cartesiansmethod.sDue to the complexity of unstructured mesh generation, as well as the highsmemory requirements and reduced accuracy of unstructured grid methods =-=[23, 25]-=-, andsthe intimate connection with image analysis techniques, we propose that an enhancedsCartesian approach is a natural route to assemble the computational components requiredsto examine the process... |

52 | A fourth order accurate discretization for the Laplace and heat equations on arbitrary domain with applications to the Stefan problem,
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Citation Context ... approach was extended to thessolution of Poisson and heat equations by Gibou et al. in [49] and later a fourth-ordersGFM scheme based on dimension-by-dimension Lagrange interpolation was proposed ins=-=[60]-=-. The concept of a ghost fluid was extended to incompressible flows by Tseng ands17sFerziger [25]. Mittal et al. [50] put forth a slight variant of the scheme proposed by Tsengsand Ferziger.sIt is wel... |

50 | Large deformation of red blood cell ghosts in a simple shear flow - Eggleton, Popel - 1998 |

46 | Patient-specific vascular nurbs modeling for isogeometric analysis of blood flow
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Citation Context ...btained from a separate simulationsMuch work has also been carried out on obtaining realistic cardiovascularsgeometries from medical images and then solving for the flow field on an unstructuredsmesh =-=[20, 21]-=- or structured curvilinear grids [22]. While this approach was successful insthese applications, extending the methodology to boundaries with large scale boundarysmotion may be difficult to manage due... |

45 | p4est: Scalable algorithms for parallel adaptive mesh refinement on forests of octrees
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Citation Context ...eometries [27]. There existsmesh refinement algorithms for Cartesian grids which scale on the largestssupercomputers currently available and which can be used to increase the efficiency ofsthe method =-=[28, 29]-=-. This thesis develops the beginning of a massively parallelsframework for solving complex moving boundary problems on Cartesian grids, enablings6sthe solution of the MHV problem along with a variety ... |

45 | An extended finite element method for two-phase fluids - Chessa, Belytschko |

45 |
Theory, algorithms, and applications of level set methods for propagating interfaces
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Citation Context ...h are represented implicitly by levelsset fields. A level set field, ϕ(x�⃗ , t), is an n+1 dimensional scalar field defined as a signedsdistance from a grid point to the nearest n-dimensional surface =-=[27, 63]-=-. The surface itselfsis embedded as the zero iso-contour of the scalar field. In this work, the level set field issmore specifically taken to be a signed normal distance function, which gives the norm... |

45 | Dynamic tubular grid: An efficient data structure and algorithms for high resolution level sets
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Citation Context ...]. In order to save computational effort and memory, theslevel set is only calculated and stored in a narrow band of grid points around the interfaces[66], or more specifically a dynamic tubular grid =-=[67]-=-. As the level set moves, the narrowsband requires rebuilding so the zero level set contour does not pass out of the domainsover which it is computed. During this rebuilding step, points that are newl... |

43 |
interface cartesian grid method i: an easily implemented technique for 3d moving boundary computations
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Citation Context ...opedsnumerical schemes based on direction-by-direction extrapolations with up to fourth-ordersspatial truncation error for the heat and Poisson equations with Dirichlet conditions, andsMarella et al. =-=[72]-=- have proposed a globally second-order solver for the solution of thes26sincompressible Navier-Stokes equations. However, stability issues often accompanysattempts to use polynomials smoother than qua... |

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Citation Context ...defined on a Lagrangian mesh are converted to volumetric forcessdefined on Cartesian flow mesh using numerical delta functions. This approach has foundsextensive use in the area of bio-fluid dynamics =-=[31, 33, 34]-=-, especially in the study ofssuspensions of flowing cells [35-37]. However, IBM has several drawbacks. First, thesnumerical delta function spreads the force over a finite support which smears the effe... |

29 |
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Citation Context ...66 ms, (b) 383 ms, (c) 400 ms, and (d) 420 ms. ..........................................159sFigure 63sThe angle of the valve leaflets versus time during valve closure for thescurrent work (line) and =-=[15]-=- (circles). The closure time is approximatelys100 ms in the current results. .........................................................................160sFigure 64sThe size of the computational grid v... |

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Citation Context ...collocated cell-centered grid,swhere the velocity and pressure are stored at cell centers and a secondary set of massconserving velocities are stored at cell faces. A four-step fractional step method =-=[69, 70]-=-sis implemented to decouple the velocity and pressure variables. In the first step, asprovisional intermediate velocity is computed for which the incompressibility constraintsis not explicitly enforce... |

25 | The extended finite element method (xfem) for solidification problems - Chessa, Smolinski, et al. |

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Citation Context ...sGFM scheme based on dimension-by-dimension Lagrange interpolation was proposed ins[60]. The concept of a ghost fluid was extended to incompressible flows by Tseng ands17sFerziger [25]. Mittal et al. =-=[50]-=- put forth a slight variant of the scheme proposed by Tsengsand Ferziger.sIt is well known that many Cartesian grid methods produce strong numericalsoscillations in the pressure field in the case of m... |

24 |
A sharp interface immersed boundary method for compressible viscous flows
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Citation Context ...eld in the case of moving boundaries due to a lack ofsgeometric volume conservation and a temporal discontinuity in the velocity field as a gridspoint changes from fluid to solid phase and vice versa =-=[30, 61, 62]-=-. While the pressuresoscillation does not significantly affect the velocity field, it can be problematic if thesmotion of a solid object is determined by the force induced by the pressure field. Kim e... |

23 | An extended finite element method for modeling crack growth with frictional contact, - Dolbow, Moes, et al. - 2001 |

23 | Design of the HYPRE preconditioner library - Chow, Cleary, et al. - 1999 |

22 | Vortex shedding as a mechanism for free emboli formation in mechanical heart valves
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Citation Context ...e flow, excessive fluid stresses are generated by the non-physiologicsflow patterns. The increased stress as well as contact of blood elements with the devicessurface may lead to blood element damage =-=[4, 5]-=-. In the closed valve position, a largespressure gradient is imposed across the device which leads to the generation of strong andsdamaging small-scale leakage flows that entrain platelets such that t... |

20 |
Extended immersed boundary method using FEM and RKPM”.
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Citation Context ... of transmitting the effect of boundaries to thesfluid through the use of source has been extended to the finite element method by thesFictitious Domain Method [41] and Immersed Finite-Element Method =-=[42]-=-.sRecently, many methods have moved away from using delta functions tosdistribute the force between grids. Instead, a forcing is derived in terms of the numericalsdiscretization scheme such that veloc... |

19 | A Numerical Method for Solving the 3D Unsteady Incompressible Navier-Stokes Equations in - Ge, Sotiropoulos - 2007 |

19 |
A remark on jump conditions for the three-dimensional Navier-Stokes equations involving an immersed moving membrane,
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Citation Context ...rs are constructed in a way such that boundarysconditions are directly incorporated into non-uniform discretization stencils. Examples ofsthis type of approach are the Immersed Interface Method (IIM) =-=[38, 46, 47]-=-, the GhostsFluid Method (GFM) [25, 48-50], the Sharp Interface Method (SIM) [51-53], and thesExtended Finite-Element Method (XFEM) [54-56]. The Immersed Interface Methodsconverts to normal and tangen... |

15 |
Free Emboli Formation in the Wake of Bi-Leaflet Mechanical Heart Valves and the Effects of Implantation Techniques,”
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Citation Context ...e flow, excessive fluid stresses are generated by the non-physiologicsflow patterns. The increased stress as well as contact of blood elements with the devicessurface may lead to blood element damage =-=[4, 5]-=-. In the closed valve position, a largespressure gradient is imposed across the device which leads to the generation of strong andsdamaging small-scale leakage flows that entrain platelets such that t... |

14 | O’Hallaron, Balance Refinement of Massive Linear Octree Datasets
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Citation Context ...n patternsis impossible as imbalances may be introduced or resolved across partition boundaries atsany time during the balancing operation. In order to address this computational challenge,sTu et al.s=-=[83]-=- proposed the Prioritized Ripple Propagation algorithm which builds on thesrealization that if cells at the finest level are balanced before cells at any coarser level, nosfuture balancing operations ... |

13 | Three-dimensional fluid-structure interaction simulation of bileaflet mechanical heart valve flow dynamics
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Citation Context ..., 15-17]. In order to attempt to elucidate the physics insthe gap region, two-dimensional and three-dimensional calculations of the leakage flowshave been carried out with simplifying assumptions. In =-=[6, 7, 18, 19]-=-, the closing phase ofsvalve motion and the associated leakage jet through the gap around the leaflet edge wassassumed to start from a quiescent condition. However, starting from a quiescent condition... |

13 | Implicit approaches for moving boundaries in a 3-D Cartesian method - Murman, Aftosmis, et al. - 2003 |

13 |
Numerical simulation of unsteady multidimensional free surface motions by level set method,”
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Citation Context ...collocated cell-centered grid,swhere the velocity and pressure are stored at cell centers and a secondary set of massconserving velocities are stored at cell faces. A four-step fractional step method =-=[69, 70]-=-sis implemented to decouple the velocity and pressure variables. In the first step, asprovisional intermediate velocity is computed for which the incompressibility constraintsis not explicitly enforce... |

12 |
Effect of exercise on hemodynamic conditions in the abdominal aorta
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Citation Context ...btained from a separate simulationsMuch work has also been carried out on obtaining realistic cardiovascularsgeometries from medical images and then solving for the flow field on an unstructuredsmesh =-=[20, 21]-=- or structured curvilinear grids [22]. While this approach was successful insthese applications, extending the methodology to boundaries with large scale boundarysmotion may be difficult to manage due... |

12 |
Numerical simulation of flow in mechanical heart valves: grid resolution and the assumption of flow symmetry
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Citation Context ... King et al. [100]sappealed to the symmetry of the valve geometry to simulate one-quarter of a valve in thesfixed position through the first half of systole up to a Reynolds number of 1500.sGe et al. =-=[101]-=- performed the first full 3D DNS simulation of a fixed valve in thesfully open position for a steady inlet condition and obtained grid-insensitive results (theslarge-scale structures are independent o... |

10 | A strictly conservative Cartesian cut-cell method for compressible viscous flows on adaptive grids - Hartmann, Meinke, et al. - 2011 |

9 |
A three-dimensional, time-dependent analysis of flow through a bileaflet mechanical heart valve: comparison of experimental and numerical results
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Citation Context ...t method. Kiris et al. [99]scomputed a RANS solution for the flow through a Bjork-Shiley valve fixed at an angle ofs143s30 degrees and the Reynolds numbers was varied from 2,000 to 6,000. King et al. =-=[100]-=-sappealed to the symmetry of the valve geometry to simulate one-quarter of a valve in thesfixed position through the first half of systole up to a Reynolds number of 1500.sGe et al. [101] performed th... |

8 | Physics-driven CFD modeling of complex anatomical cardiovascular flows—A TCPC case study. Annals of biomedical engineering
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Citation Context ...ork has also been carried out on obtaining realistic cardiovascularsgeometries from medical images and then solving for the flow field on an unstructuredsmesh [20, 21] or structured curvilinear grids =-=[22]-=-. While this approach was successful insthese applications, extending the methodology to boundaries with large scale boundarysmotion may be difficult to manage due to the complexity of generating high... |

8 | Interface tracking finite volume method for complex solid–fluid interactions on fixed meshes - Udaykumar, Mittal, et al. |

7 |
Turbulence characteristics downstream of bileaflet aortic valve prostheses
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Citation Context ...ack of consensus in the literature about which flow scales are mostsdamaging to cells. In [9] and [10] it is argued that it is the energetic middle-range flowsstructures that are most damaging, while =-=[11, 12]-=- propose that it is in fact the smallestsstructures that are responsible for blood element damage. Furthermore, it is still unclears3swhat the smallest scale is that exists in the MHV flow field. Duri... |

7 |
High-resolution fluid–structure interaction simulations of flow through a bi-leaflet mechanical heart valve in an anatomic aorta
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(Show Context)
Citation Context ...mpletely resolved all gapsregions. Several studies have been undertaken to try to quantify the flow physics in thesgaps. Most notably, Simon et al. [8] have used the large-scale simulation results of =-=[16]-=- tossupply boundary conditions for a simulation at the scale of the hinge region of a St.sJude’s mechanical heart valve. It was demonstrated that the shear stress in the hingesregion is much higher du... |

7 | Developments in Cartesian cut cell methods. - Ingram, Causon, et al. - 2003 |

6 | A convergence study of a new partitioned fluid–structure interaction algorithm based on fictitious mass and damping. - Baek, Karniadakis - 2012 |

5 |
Two-dimensional fluid-structure interaction simulation of bileaflet mechanical heart valve flow dynamics. The Journal of heart valve disease
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- 2003
(Show Context)
Citation Context ..., 15-17]. In order to attempt to elucidate the physics insthe gap region, two-dimensional and three-dimensional calculations of the leakage flowshave been carried out with simplifying assumptions. In =-=[6, 7, 18, 19]-=-, the closing phase ofsvalve motion and the associated leakage jet through the gap around the leaflet edge wassassumed to start from a quiescent condition. However, starting from a quiescent condition... |

5 |
Models of flow-induced loading on blood cells in laminar and turbulent flow, with application to cardiovascular device flow. Annals of biomedical engineering
- Quinlan, Dooley
- 2007
(Show Context)
Citation Context ...cations of mechanical heart valves include leakages, infections,sand tissue overgrowth [2].sThere is still a lack of consensus in the literature about which flow scales are mostsdamaging to cells. In =-=[9]-=- and [10] it is argued that it is the energetic middle-range flowsstructures that are most damaging, while [11, 12] propose that it is in fact the smallestsstructures that are responsible for blood el... |

5 | Sharp-interface simulation of dendritic growth with convection: benchmarks. International journal of heat and mass transfer - Udaykumar, Marella, et al. - 2003 |

5 | Low-cost parallel algorithms for 2: 1 octree balance - Isaac, Burstedde, et al. |

5 |
A finite element analysis of the steady laminar entrance flow in a 90 curved tube. International journal for numerical methods in fluids
- Vosse
(Show Context)
Citation Context ...ysmagnitude is plotted on the center-plane and streamlines are plotted tosindicate the presence of a secondary flow. The axial velocity at the bendsoutlet is compared with the experimental results of =-=[95]-=- in (c). ....................136sFigure 49sA schematic of the human larynx. The upstream and downstreamschannels are separated by a complex flap system which induces the jetsflow required for sound pr... |

5 |
Computational Approach for Probing the Flow Through Artificial Heart Devices,’’
- Kiris, Kwak, et al.
- 1997
(Show Context)
Citation Context ...y on the basis of the symmetry ofsthe prosthesis. Shim and Chang [97] examined static tilting-disk and Bjork-Shiley [98]svalves in the half-open position using the finite-element method. Kiris et al. =-=[99]-=-scomputed a RANS solution for the flow through a Bjork-Shiley valve fixed at an angle ofs143s30 degrees and the Reynolds numbers was varied from 2,000 to 6,000. King et al. [100]sappealed to the symme... |

4 |
Numerical simulation of the dynamics of a bileaflet prosthetic heart valve using a fluid-structure interaction approach
- Nobili, Morbiducci, et al.
- 2008
(Show Context)
Citation Context ...ynolds number of approximately 6,000sand a mean Reynolds number of nearly 4000, which results in an estimate of 0.04 ands0.06 mm as the size of the smallest flow structures based on Kolmogorov theory =-=[13]-=-.sWhile the assumptions of Kolmogorov theory are not applicable due to the short transientsnature of the MHV flow field, Bellofiore and Quinlan [14] used PIV to establish thatsthere exists structures ... |

4 |
On the numerical oscillation of the direct-forcing immersedboundary method for moving boundaries
- Luo
(Show Context)
Citation Context .... The required locations of the interface where boundarysconditions are required are easily computed with high accuracy using the level setsrepresentation.sFollowing an approach similar to Luo et al. =-=[30]-=-, a hybridization of the method issdeveloped such that grid points smoothly transition between solving the governingsequations and being populated by extrapolation techniques as the surface evolves. T... |

4 | Computational analysis of the deformability of leukocytes modeled with viscous and elastic structural components. - Marella, Udaykumar - 2004 |

4 |
Sources of spurious force oscillations from an immersed boundary method for moving-body problems
- LEE, KIM, et al.
- 2011
(Show Context)
Citation Context ...eld in the case of moving boundaries due to a lack ofsgeometric volume conservation and a temporal discontinuity in the velocity field as a gridspoint changes from fluid to solid phase and vice versa =-=[30, 61, 62]-=-. While the pressuresoscillation does not significantly affect the velocity field, it can be problematic if thesmotion of a solid object is determined by the force induced by the pressure field. Kim e... |

4 |
Metis/Parmetis web page,
- Karypis
- 2008
(Show Context)
Citation Context ...rocess of locating thesclosest grid point to an arbitrary location can be performed in a straight-forward andsefficient manner.sContinuity of numbering on partitions is required by the PETSc [81] and =-=[82]-=-sParMETIS libraries, which are used by pELAFINT3D to solve linear systems andscompute load-balanced partitions. Consequently, a second global numbering is assignedswhich will be called the application... |

3 |
Two-dimensional dynamic simulation of platelet activation during mechanical heart valve closure. Annals of biomedical engineering
- Krishnan
- 2006
(Show Context)
Citation Context ..., 15-17]. In order to attempt to elucidate the physics insthe gap region, two-dimensional and three-dimensional calculations of the leakage flowshave been carried out with simplifying assumptions. In =-=[6, 7, 18, 19]-=-, the closing phase ofsvalve motion and the associated leakage jet through the gap around the leaflet edge wassassumed to start from a quiescent condition. However, starting from a quiescent condition... |

3 |
Prosthesis-induced hemolysis: mechanisms and quantification of shear stress. The Journal of heart valve disease
- Ellis, Wick, et al.
- 1998
(Show Context)
Citation Context ...ack of consensus in the literature about which flow scales are mostsdamaging to cells. In [9] and [10] it is argued that it is the energetic middle-range flowsstructures that are most damaging, while =-=[11, 12]-=- propose that it is in fact the smallestsstructures that are responsible for blood element damage. Furthermore, it is still unclears3swhat the smallest scale is that exists in the MHV flow field. Duri... |

3 |
Individualized computer-based surgical planning to address pulmonary arteriovenous malformations in patients with a single ventricle with an interrupted inferior vena cava and azygous continuation. The Journal of thoracic and cardiovascular surgery
- Zélicourt
- 2011
(Show Context)
Citation Context ...nsthese applications, extending the methodology to boundaries with large scale boundarysmotion may be difficult to manage due to the complexity of generating high qualitysunstructured meshes [23]. In =-=[24]-=-, patient specific cardiovascular geometries weresobtained from medical images and the flow fields were subsequently computed using ansunstructured Cartesian approach with a reduced memory footprint. ... |

2 | Numerical Investigation of the Performance of Three Hinge Designs of Bileaflet Mechanical Heart Valves. Annals of biomedical engineering
- Simon
(Show Context)
Citation Context ...vice which leads to the generation of strong andsdamaging small-scale leakage flows that entrain platelets such that they are exposed toselevated stresses for a extended durations [6-8]. Simon et al. =-=[8]-=- performed numericalssimulations of leakage flow in the hinge region of a St. Jude mechanical valve and foundsthat platelet activation and thrombus formation was likely to occur near the hinge regions... |

2 |
Parallel multi-physics AMR applications using the SAMRAI Library
- Wissink
(Show Context)
Citation Context ...eometries [27]. There existsmesh refinement algorithms for Cartesian grids which scale on the largestssupercomputers currently available and which can be used to increase the efficiency ofsthe method =-=[28, 29]-=-. This thesis develops the beginning of a massively parallelsframework for solving complex moving boundary problems on Cartesian grids, enablings6sthe solution of the MHV problem along with a variety ... |

2 |
Three-dimensional vortex flow past a tilting disc valve using a segregated finite element scheme
- Shim, Chang
- 1994
(Show Context)
Citation Context ...he inlet condition lacks pulsatility. Additionally, sometimes the simulations weresperformed on reduced portions of the full 3D geometry on the basis of the symmetry ofsthe prosthesis. Shim and Chang =-=[97]-=- examined static tilting-disk and Bjork-Shiley [98]svalves in the half-open position using the finite-element method. Kiris et al. [99]scomputed a RANS solution for the flow through a Bjork-Shiley val... |

1 |
Biofluid mechanics: the human circulation. 2007
- Chandran, Rittgers, et al.
(Show Context)
Citation Context ... heart valves (BHV).sThe most commonly used mechanical valves, accounting for 80% of mechanicalsprosthesis replacements, are based on the bileaflet design introduced by St. Jude Medical,sInc. in 1978 =-=[2]-=-. The St. Jude Medical valve design, which is shown in Figure 1, has twospyrolytic carbon leaflets which rotate within a hinge recess in a surrounding valveshousing. In the fully open position, the le... |

1 |
The Worldwide Mid-Term Experience with the Medtronic ADVANTAGE? Bileaflet Mechanical Heart Valve
- Korfer
(Show Context)
Citation Context ...Even after half a century of use, mechanical heart valves still require furthersresearch to reduce the non-physiologic nature of the flow field, which is the source ofspotential medical complications =-=[3]-=-, of which the most serious complications includesthrombus formation due to blood element trauma and subsequent device failure [2]. In thessystolic phase of the flow, excessive fluid stresses are gene... |

1 |
Effect of eddy length scale on mechanical loading of blood cells in turbulent flow. Annals of biomedical engineering
- Dooley, Quinlan
(Show Context)
Citation Context ...of mechanical heart valves include leakages, infections,sand tissue overgrowth [2].sThere is still a lack of consensus in the literature about which flow scales are mostsdamaging to cells. In [9] and =-=[10]-=- it is argued that it is the energetic middle-range flowsstructures that are most damaging, while [11, 12] propose that it is in fact the smallestsstructures that are responsible for blood element dam... |

1 |
High-Resolution Measurement of the Unsteady Velocity Field to Evaluate Blood Damage Induced by a Mechanical Heart Valve. Annals of biomedical engineering
- Bellofiore, Quinlan
- 2011
(Show Context)
Citation Context ...smallest flow structures based on Kolmogorov theory [13].sWhile the assumptions of Kolmogorov theory are not applicable due to the short transientsnature of the MHV flow field, Bellofiore and Quinlan =-=[14]-=- used PIV to establish thatsthere exists structures blood damaging smaller than 0.120 mm in the forward flow phase.sDuring diastole, the jets occurring due to the leakage flow are of the scale of the ... |

1 |
Pressure field in the vicinity of mechanical valve occluders at the instant of valve closure: correlation with cavitation initiation. The Journal of heart valve disease
- Chandran, Lee, et al.
- 1994
(Show Context)
Citation Context |

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Flow simulations in arbitrarily complex cardiovascular anatomies–An unstructured Cartesian grid approach
- Zélicourt
(Show Context)
Citation Context ...required to compute the evolution of a quantity are stored on a sparse tube ofsrectangular grid cells only where necessary. This concept was extended to a Cartesiansgrid solver by de Zelicourt et al. =-=[80]-=-. However, to our knowledge, the DTG approach hassnot been enhanced with local mesh refinement and massive parallelization in the contextsof a Cartesian grid solver.sAn example of a mesh generated by ... |

1 |
PETSc Users Manual Revision 3.2
- Balay
- 2011
(Show Context)
Citation Context ...hat the process of locating thesclosest grid point to an arbitrary location can be performed in a straight-forward andsefficient manner.sContinuity of numbering on partitions is required by the PETSc =-=[81]-=- and [82]sParMETIS libraries, which are used by pELAFINT3D to solve linear systems andscompute load-balanced partitions. Consequently, a second global numbering is assignedswhich will be called the ap... |

1 |
An adaptively refined Cartesian grid method for moving boundary problems applied to biomedical systems
- Krishnan
- 2006
(Show Context)
Citation Context ...of the discretization on thesconvergence rate of matrix problems does not need to be considered. In the current work,sconvective fluxes are computed using a conservative bilinear interpolation scheme =-=[86]-=-.sAgain, the starting point for the numerical scheme is the finite-volume form of thesconvective term:s∫∇ ∙ (... |

1 | Vortex dynamics in the sphere - Mittal, Najjar - 1999 |

1 |
Vortex dipolar structures in a rigid model of the larynx at flow onset. Experiments in Fluids
- Chisari, Artana, et al.
- 2011
(Show Context)
Citation Context ...lap system which induces the jetsflow required for sound production. ..............................................................137sFigure 50sThe representative vocal fold geometry replicated from =-=[96]-=-. The secondsconstriction gap is twice that of the first constriction. ...................................137sxiiisFigure 51sA comparison of vorticity contours for the current results (left) with thes... |

1 |
Numerical analysis of three-dimensional Björk– Shiley valvular flow in an aorta
- Shim, Chang
- 1997
(Show Context)
Citation Context ... sometimes the simulations weresperformed on reduced portions of the full 3D geometry on the basis of the symmetry ofsthe prosthesis. Shim and Chang [97] examined static tilting-disk and Bjork-Shiley =-=[98]-=-svalves in the half-open position using the finite-element method. Kiris et al. [99]scomputed a RANS solution for the flow through a Bjork-Shiley valve fixed at an angle ofs143s30 degrees and the Reyn... |