A differentially interpolated direct forcing immersed boundary method for predicting incompressible Navier–Stokes equations in time-varying complex geometries

Chiu, Pao‐Hsiung; Lin, R. K.; Sheu, Tony W. H.

doi:10.1016/j.jcp.2010.02.013

Cited by 51 publications

(28 citation statements)

References 54 publications

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“…The results for the Strouhal number, the lift fluctuations as well as the drag are presented in table 1. They are presented alongside data available in the literature from experiments [37,38], body-fitted simulations [31,32,33] and other IMBMs [34,35,36,18]. Given the scatter among the reported results the data obtained from simulations with the BDIM agree reasonably well with the values from literature.…”

Section: Assessment Of Accuracysupporting

confidence: 68%

The boundary data immersion method for compressible flows with application to aeroacoustics

Schlanderer

Weymouth

Sandberg

2017

Journal of Computational Physics

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This paper introduces a virtual boundary method for compressible viscous fluid flow that is capable of accurately representing moving bodies in flow and aeroacoustic simulations. The method is the compressible extension of the boundary data immersion method (BDIM, Maertens & Weymouth (2015)). The BDIM equations for the compressible Navier-Stokes equations are derived and the accuracy of the method for the hydrodynamic representation of solid bodies is demonstrated with challenging test cases, including a fully turbulent boundary layer flow and a supersonic instability wave. In addition we show that the compressible BDIM is able to accurately represent noise radiation from moving bodies and flow induced noise generation without any penalty in allowable time step.

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Section: Assessment Of Accuracysupporting

confidence: 68%

The boundary data immersion method for compressible flows with application to aeroacoustics

Schlanderer

Weymouth

Sandberg

2017

Journal of Computational Physics

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“…The mean drag (C D ) and lift (C L ) coefficients calculated using the DIK method, as well as the individual contribution from pressure and friction (indicated by subscripts p and f respectively) are compared to body-fitted simulations from Park [33] and Henderson [34] in Table 1. In the same table, results are also compared to other Cartesian-grid methods [35,36] and experimental measurements [31,32]. For this simple geometry low Reynolds number example, both 1st and 2nd order BDIM compare well with documented results, validating the force calculation approach.…”

Section: Two-dimensional Flow Past a Stationary Cylinder At Low Reynomentioning

confidence: 58%

Accurate Cartesian-grid simulations of near-body flows at intermediate Reynolds numbers

Maertens

Weymouth

2015

Computer Methods in Applied Mechanics and Engineering

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An accurate Cartesian-grid treatment for intermediate Reynolds number fluid-solid interaction problems is described. We first identify the inability of existing immersed boundary methods to handle intermediate Reynolds number flows to be the discontinuity of the velocity gradient at the interface. We address this issue by generalizing the Boundary Data Immersion Method (BDIM, Weymouth and Yue, J. Comp. Phys., vol. 230, 2011), in which the field equations of each domain are combined analytically, through the addition of a higher order term to the integral formulation. The new method, featuring a second-order convolution, retains the desirable simplicity of direct forcing methods and smoothes the velocity field at the fluid-solid interface while removing its bias. This results in accurate flow predictions and pressure fields without spurious fluctuations, even at high Reynolds number where the method is second order in the L 2 norm. A treatment for sharp corners is also derived that significantly improves the flow predictions near the trailing edge of thin airfoils. The second-order BDIM is applied to unsteady problems relevant to ocean energy extraction as well as animal and vehicle locomotion for Reynolds numbers up to 10 5 .

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“…Among them, the most widely employed to improve the accuracy of the solution close to Σ h are those based on an interpolation or extrapolation procedure (e.g. [9][10][11][12][13]25]). Roughly speaking, the interpolation or extrapolation procedures involve solid and fluid velocity contributions to calculate the velocities at the forcing nodes.…”

Section: Reconstruction Of the Velocity Field : Interpolation Schemesmentioning

confidence: 99%

“…Since its development by Mohd-Yusof [8], the DF method has gained in popularity and has been successfully applied to various fluid-structure interaction problems (e.g. [10][11][12][13][14][15]) or turbulent flow simulations (e.g. [16,17]) using mesh refinement or mesh stretching techniques.…”

Section: Introductionmentioning

confidence: 99%

A second order penalized direct forcing for hybrid Cartesian/immersed boundary flow simulations

Introini¹,

Belliard²,

Fournier³

2014

Computers & Fluids

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In this paper, we propose a second order penalized direct forcing method to deal with fluidstructure interaction problems involving complex static or time-varying geometries. As this work constitutes a first step toward more complicated problems, our developments are restricted to Dirichlet boundary condition in purely hydraulic context. The proposed method belongs to the class of immersed boundary techniques and consists in immersing the physical domain in a Cartesian fictitious one of simpler geometry on fixed grids. A penalized forcing term is added to the momentum equation to take the boundary conditions around/inside the obstacles into account. This approach avoids the tedious task of re-meshing and allows us to use fast and accurate numerical schemes. In contrary, as the immersed boundary is described by a set of Lagrangian points that does not generally coincide with those of the Eulerian grid, numerical procedures are required to reconstruct the velocity field near the immersed boundary. Here, we develop a second order linear interpolation scheme and we compare it to a simpler model of order one. As far as the governing equations are concerned, we use a particular fractional-step method in which the penalized forcing term is distributed both in prediction and correction equations. The accuracy of the proposed method is assessed through 2-D numerical experiments involving static and rotating solids. We show in particular that the numerical rate of convergence of our method is quasi-quadratic.

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A differentially interpolated direct forcing immersed boundary method for predicting incompressible Navier–Stokes equations in time-varying complex geometries

Cited by 51 publications

References 54 publications

The boundary data immersion method for compressible flows with application to aeroacoustics

The boundary data immersion method for compressible flows with application to aeroacoustics

Accurate Cartesian-grid simulations of near-body flows at intermediate Reynolds numbers

A second order penalized direct forcing for hybrid Cartesian/immersed boundary flow simulations

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