A Vortex/Impulse Method for Immersed Boundary Motion in High Reynolds Number Flows

Cortez, Ricardo

doi:10.1006/jcph.2000.6474

Cited by 11 publications

(8 citation statements)

References 23 publications

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“…Several approaches to this problem have been and are being tried. The IB method has been combined with vortex methods (McCracken andPeskin 1980, Peskin 1981), with impulse methods (Cortez 1996, Cortez and Varela 1997, Cortez 2000, and with adaptive mesh refinement (Roma et al 1999).…”

Section: Research Directionsmentioning

confidence: 99%

The immersed boundary method

2002

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Like many problems in biofluid mechanics, cardiac mechanics can be modeled as the dynamic interaction of a viscous incompressible fluid (the blood) and a (visco-)elastic structure (the muscular walls and the valves of the heart). The immersed boundary method is a mathematical formulation and numerical approach to such problems that was originally introduced to study blood flow through heart valves, and extensions of this work have yielded a three-dimensional model of the heart and great vessels. In the present work, we introduce a new adaptive version of the immersed boundary method. This adaptive scheme employs the same hierarchical structured grid approach (but a different numerical scheme) as the twodimensional adaptive immersed boundary method of Roma et al. [A multilevel self adaptive version of the immersed boundary method, Ph.D. Thesis, Courant Institute of Mathematical Sciences, New York University, 1996; An adaptive version of the immersed boundary method, J. Comput. Phys. 153 (2) (1999) 509-534] and is based on a formally second order accurate (i.e., second order accurate for problems with sufficiently smooth solutions) version of the immersed boundary method that we have recently described [B.E. Griffith, C.S. Peskin, On the order of accuracy of the immersed boundary method: higher order convergence rates for sufficiently smooth problems, J. Comput. Phys. 208 (1) (2005) 75-105]. Actual second order convergence rates are obtained for both the uniform and adaptive methods by considering the interaction of a viscous incompressible flow and an anisotropic incompressible viscoelastic shell. We also present initial results from the application of this methodology to the three-dimensional simulation of blood flow in the heart and great vessels. The results obtained by the adaptive method show good qualitative agreement with simulation results obtained by earlier non-adaptive versions of the method, but the flow in the vicinity of the model heart valves indicates that the new methodology provides enhanced boundary layer resolution. Differences are also observed in the flow about the mitral valve leaflets. Ó 2006 Elsevier Inc. All rights reserved.MSC: 65M06; 65M50; 74S20; 76D05; 92C10; 92C35

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Section: Research Directionsmentioning

confidence: 99%

The immersed boundary method

2002

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“…The reason for doing so is that, as m evolves, it may develop finer spatial scales than those exhibited in the physical velocity field u , which may subsequently require unnecessary spatial resolution to resolve. This phenomenon has also been observed in single-phase gauge methods ( 18 , 23 , 24 , 26 , 40 ), where it has been noted that the norm of m may grow in time without bound (depending on the dynamics taking place). For the examples presented in this work, the capillary wave dynamics ( Figs.…”

Section: Discussionmentioning

confidence: 55%

Interfacial gauge methods for incompressible fluid dynamics

Saye

2016

Sci. Adv.

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“…Line 11 of the pseudo code in listing 1 describes the interpolation of the fiber velocity in terms of equation (22). When combined with equation (25), the fibers are repositioned to their new points in space.…”

Section: C O N S T I N T I S T O P = I S T a R T + 4 ;mentioning

confidence: 99%

“…We shall not attempt to compare these methods here; instead we list some of them for readers' reference. These methods include immersed boundary (IB) methods [5,20], the immersed interface methods [21], blob-projection [22], immersed continuum [23], and immersed finite element [24], the Arbitrary Lagrangian Eulerian (ALE) [27], the fictitious domain method [25], the material point method [26], the level set method [72], and the front tracking method [71].…”

Section: Introductionmentioning

confidence: 99%

Interactive 3D simulation for fluid–structure interactions using dual coupled GPUs

2017

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The scope of this work involves the integration of high speed parallel computation with interactive, 3D visualization of the lattice-Boltzmannbased immersed boundary method for fluid-structure-interaction. An NVIDIA Tesla K40c is used for the computations while an NVIDIA Quadro K5000 is used for 3D vector field visualization. The simulation can be paused at any time step so that the vector field can be explored. The density and placement of streamlines and glyphs are adjustable by the user, while panning and zooming is controlled by the mouse. The simulation can then be resumed. Unlike most scientific applications in computational fluid dynamics where visualization is performed after the computations, our software allows for real-time visualizations of the flow fields while the computations take place. To the best of our knowledge, such a tool on GPUs for FSI does not exist. Our software can facilitate debugging, enable observation of detailed local fields of flow and deformation while computing, and expedite identification of 'correct' parameter combinations in parametric studies for new phenomenon. Therefore, our software is expected to shorten the 'time to solution' process and expedite the scientific discoveries via scientific computing.Keywords lattice Boltzmann method · the immersed boundary method · GPU computing · fluid structure interaction(FSI) · interactive simulation · real time visualization

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A Vortex/Impulse Method for Immersed Boundary Motion in High Reynolds Number Flows

Cited by 11 publications

References 23 publications

The immersed boundary method

The immersed boundary method

Interfacial gauge methods for incompressible fluid dynamics

Interactive 3D simulation for fluid–structure interactions using dual coupled GPUs

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