Discrete lattice effect of various forcing methods of body force on immersed Boundary-Lattice Boltzmann method

Son, Sung Wan; Yoon, Hyun Sik; Jeong, Hae Kwon; Ha, Man Yeong; Balachandar, S.

doi:10.1007/s12206-012-1256-z

Cited by 5 publications

(4 citation statements)

References 34 publications

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“…Consequently, it can correctly recover equations ( 1) and ( 2) by a Chapman-Enskog multi-scale expansion with second-order accuracy for either steady flow or unsteady flow, and either uniform external force or non-uniform external force. This was further confirmed by Son et al [26]. The Guo et al [25] model has been widely applied in fluid-structure interaction flows.…”

Section: Governing Equationsmentioning

confidence: 60%

“…drs N (26) As can be seen in equations (26), (25) and (22), drs is decided by the regularized delta function δij (· ) and the Lagrangian points step ds, which will be depicted in Section 4.4.…”

Section: Boundary Thickening Direct Forcingmentioning

confidence: 99%

“…In addition, the curve profile of the 2-point delta function is severely oscillating due to the linear interpolation property of this function, while the curve profile of the 3-and 4-point delta functions are more smoothing because these two functions are smoothing. Then these local values are averaged to a uniform thickness value according to the physical meaning with a minimum error by equation (26), as shown in Fig.4. Figure 4 illustrates the value of drs/dh varying with the different delta functions, i.e., drf/dh, Eulerian grids solution D/dh, and Lagrangian points spacing ds/dh.…”

Section: The Thickness Of the Solid Forcing Shell Drsmentioning

confidence: 99%

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A boundary thickening-based direct forcing immersed boundary method for fully resolved simulation of particle-laden flows

Jiang

Liu

2019

Journal of Computational Physics

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A boundary thickening-based direct forcing (BTDF) immersed boundary (IB) method is proposed for fully resolved simulation of incompressible viscous flows laden with finite size particles. By slightly thickening the boundary thickness, the local communication between the Lagrangian points on the solid boundary and their neighboring fluid Eulerian grids is improved, based on an implicit direct forcing (IDF) approach and a partition-of-unity condition for the regularized delta function. This strategy yields a simple, yet much better imposition of the no-slip and no-penetration boundary conditions than the conventional direct forcing (DF) technique. In particular, the present BTDF method can achieve a numerical accuracy comparable with other representative improved methods, such as multi-direct forcing (MDF), implicit velocity correction (IVC) and the reproducing kernel particle method (RKPM), while its computation cost remains much lower and nearly equivalent to the conventional DF scheme. The dependence of the optimum thickness value of boundary thickening on the form of the regularized delta functions is also revealed. By coupling the lattice Boltzmann method (LBM) with BTDF-IB, the robustness of the present BTDF IB method is demonstrated using numerical simulations of creeping flow (Re=0.1), steady vortex separating flow (Re=40) and unsteady vortex shedding flow (Re=200) around a circular cylinder.

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Section: Governing Equationsmentioning

confidence: 60%

Section: Boundary Thickening Direct Forcingmentioning

confidence: 99%

Section: The Thickness Of the Solid Forcing Shell Drsmentioning

confidence: 99%

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A boundary thickening-based direct forcing immersed boundary method for fully resolved simulation of particle-laden flows

Jiang

Liu

2019

Journal of Computational Physics

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“…The schemes considering the collision effect (ie, the BG and GZS schemes) perform slightly better than those without consideration of the effect (ie, the WFM/HM and L/M schemes) in terms of the accuracy of velocity (Table 1), which is consistent with the previous studies. 28,39,48 Besides, the comparison between the WFM/HM coupled with the two LB models (the first and second row in Table 1) shows that the combination of the hydrostatic pressure gradient and the bed slope indeed minimizes the discretization error and makes MLBSWE prone to produce more accurate solutions when the forcing schemes are used to deal with the effect of the bed elevation, 18 although the discrepancy is not so remarkable.…”

Section: Accuracymentioning

confidence: 99%

An evaluation of force terms in the lattice Boltzmann models in simulating shallow water flows over complex topography

Zeng

et al. 2019

Numerical Methods in Fluids

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Summary Proper approximation of the force terms, especially the bed slope term, is of crucial importance to simulating shallow water flows in lattice Boltzmann (LB) models. However, there is little discussion on the schemes of adding force terms to LB models for shallow water equations (SWEs). In this study, we evaluate the performance of forcing schemes coupled with different LB models (LABSWE and MLBSWE) in simulating shallow water flows over complex topography and try to find out their intrinsic characteristics and applicability. Three cases are adopted for evaluation, including a stationary case, a one‐dimensional tidal wave flow over an irregular bed, and a steady flow over a two‐dimensional seamount. The simulating results are compared with analytical solutions or the results produced by the finite difference method. For LABSWE, all the forcing schemes, except for the weighting factor method, fail to produce accurate solutions for the test cases; this is probably due to the mismatch between the bed slope term in source terms and the quadratic depth term of the equilibrium distribution functions in these forcing schemes. For MLBSWE, all the forcing schemes are capable of simulating flows over the complex topography accurately; furthermore, those schemes taking into account the collision effect τ to eliminate the momentum induced by forces provide more accurate solutions with quicker convergence as the lattice size decreases. In this view, MLBSWE can bring more flexibility in treating the force terms and thus can be a better tool to simulate shallow water flows over complex topography in practical application.

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Lattice BGK simulations of the double diffusive mixed convection in an enclosure with different outlet locations

Chen

et al. 2016

International Journal of Heat and Mass Transfer

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Discrete lattice effect of various forcing methods of body force on immersed Boundary-Lattice Boltzmann method

Cited by 5 publications

References 34 publications

A boundary thickening-based direct forcing immersed boundary method for fully resolved simulation of particle-laden flows

A boundary thickening-based direct forcing immersed boundary method for fully resolved simulation of particle-laden flows

An evaluation of force terms in the lattice Boltzmann models in simulating shallow water flows over complex topography

Lattice BGK simulations of the double diffusive mixed convection in an enclosure with different outlet locations

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