An Immersed Boundary Method with Formal Second-Order Accuracy and Reduced Numerical Viscosity

Lai, Ming-Chih; Peskin, Charles S.

doi:10.1006/jcph.2000.6483

Cited by 791 publications

(556 citation statements)

References 23 publications

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“…This method was firstly applied to steady forces by Lai and Peskin [3], and later, it was extended to unsteady forces by Balaras [4] and to moving body problems by Shen et al [5]. The control volume method has an advantage that it is unnecessary to directly handle the complex geometries expressed by the immersed boundaries.…”

Section: Introductionmentioning

confidence: 99%

A Comparative Study on Evaluation Methods of Fluid Forces on Cartesian Grids

Nonomura¹,

Onishi

2017

Mathematical Problems in Engineering

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We investigate the accuracy and the computational efficiency of the numerical schemes for evaluating fluid forces in Cartesian grid systems. A comparison is made between two different types of schemes, namely, polygon-based methods and mesh-based methods, which differ in the discretization of the surface of the object. The present assessment is intended to investigate the effects of the Reynolds number, the object motion, and the complexity of the object surface. The results show that the mesh-based methods work as well as the polygon-based methods, even if the object surface is discretized in a staircase manner. In addition, the results also show that the accuracy of the mesh-based methods is strongly dependent on the evaluation of shear stresses, and thus they must be evaluated by using a reliable method, such as the ghost-cell or ghost-fluid method.

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Section: Introductionmentioning

confidence: 99%

A Comparative Study on Evaluation Methods of Fluid Forces on Cartesian Grids

Nonomura¹,

Onishi

2017

Mathematical Problems in Engineering

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“…After the interpolation coefficients are all available, the velocity and pressure at the forcing point 0 0 ( , ) x y are determined by 11 12 …”

Section: The Implicit Virtual Boundary Methodsmentioning

confidence: 99%

“…(5), (11), and (18) are solved with the strongly implicit solver [29]. The numerical procedure described in this section is called the NAPPLE algorithm [30].…”

Section: Brief Review Of the Napple Algorithmmentioning

confidence: 99%

“…The main concept of this particular numerical method is to impose an external force field at the fluid grid points adjacent to the solid boundary in the same manner as would the solid boundary. This branch of numerical methods was studied extensively for biological flow, multi-phase flow and problems with elastic boundary [6][7][8][9][10][11][12]. One of the major drawbacks of the immersed-boundary method is the smoothing of the external force field that could lead to smearing of interface information.…”

Section: Introductionmentioning

confidence: 99%

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Implicit Virtual Boundary Method for Moving Boundary Problems on Non-Staggered Cartesian Patch Grids

2017

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A simple numerical method is proposed in the paper for fluid flow around a moving boundary of irregular shape. The unsteady term is discretized with the implicit scheme such that large time step is allowed. All of the computations are performed on non-staggered Cartesian grid system. Fine Cartesian patch grid system covering the moving object is employed to resolve the solution around the solid body. A closed curve defined by connecting the solid grid points adjacent to the solid-liquid interface is referred to as virtual boundary. The narrow irregular strip of solid between the virtual boundary and the actual solid-fluid interface is called pseudo-fluid. The general fluid region consisting of both fluid and pseudo-fluid is a regular domain that can be efficiently solved with conventional numerical method. In this connection, external force is imposed at each fluid grid point adjacent to the solid-fluid interface to compensate for the numerical error arising from the assumption of pseudo-fluid. The solution procedure is iterated until the required external force converges. Accuracy of the new numerical method is validated through three test problems. The numerical method then is used to investigate the flow induced by the flapping wings of a tethered dragonfly in literature. The corresponding CFL numbers of the four examples are infinity, 20, 100, and 3.29.

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“…Within the IB method, there too exists different versions. Examples include the original versions [4], the vortex-method version [29], the volume-conserved version [30], the adaptive mesh refinement version [31], the (formally) second-order versions [33,34], the multigrid version [35], the penalty version [36], the implicit versions [37-39, 42, 43], the generalized version for a thick rod [44], the stochastic version [45], the porous media version, the lattice-Boltzmann version [3,48,49,60,61,[53][54][55][56]59,63], the fluid-solute-structure interaction version [50], and the variable viscosity version [52].…”

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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An Immersed Boundary Method with Formal Second-Order Accuracy and Reduced Numerical Viscosity

Cited by 791 publications

References 23 publications

A Comparative Study on Evaluation Methods of Fluid Forces on Cartesian Grids

A Comparative Study on Evaluation Methods of Fluid Forces on Cartesian Grids

Implicit Virtual Boundary Method for Moving Boundary Problems on Non-Staggered Cartesian Patch Grids

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

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