Hydrodynamic Force Evaluation by Momentum Exchange Method in Lattice Boltzmann Simulations

Wen, Binghai; Zhang, Chaoying; Fang, Haiping

doi:10.3390/e17127876

Cited by 27 publications

(18 citation statements)

References 97 publications

(250 reference statements)

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“…Originating from the cellular automaton concept and kinetic theory, the intrinsic mesoscopic properties make lattice Boltzmann method (LBM) outstanding in modeling complex fluid systems involving interfacial dynamics [23][24][25] and phase transitions [7,8]. In basic approach of LBM, a particle distribution function is used to depict the behavior of the multiphase flows, which obeys the following lattice Boltzmann equation…”

Section: Pseudopotential Modelsmentioning

confidence: 99%

A pseudopotential multiphase lattice Boltzmann model based on high-order difference

Qin

Zhao

Chen

et al. 2018

International Journal of Heat and Mass Transfer

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The hyperbolic tangent function is usually used as a reliable approximation of the equilibrium density distributions of a system with phase transitions. However, analyzing the accuracies of the numerical derivatives, we find that its numerical derivatives computed by central difference method (CDM) may deviate significantly from its analytical solutions, while those computed by high-order difference method (HDM) can agree very well. Therefore, we introduce HDM to evaluate the interparticle interactions instead of popular CDM, and propose a pseudopotential multiphase lattice Boltzmann model based on high-order difference method. The present model not only retains the advantages of the pseudopotential model, such as easy implementation, high efficiency, full parallelism and so on, but also achieves higher accuracies. To verify the performances of this model, several multiphase flow simulations are conducted, including both stationary and dynamic situations. Firstly, full thermodynamic consistencies for the popular equations of state have been achieved in large temperature range and at large density ratio, without any combining interaction and any additional adjustable parameter of interaction. Secondly, with high-order difference, either the interparticle interaction proposed by Shan-Chen or by Zhang-Chen can equally depict the phase transitions of the fluids with all selected equations of the state. These numerical * Corresponding authors.agreements based on HDM are consistent to the theoretical analysis that the two models are mathematically identical. Thirdly, the present model is stable and accurate at a wider temperature range. Lastly, our newly proposed model can be easily and reliably applied to various practical simulations and expected to obtain some more interesting results.

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Section: Pseudopotential Modelsmentioning

confidence: 99%

A pseudopotential multiphase lattice Boltzmann model based on high-order difference

Qin

Zhao

Chen

et al. 2018

International Journal of Heat and Mass Transfer

Self Cite

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“…[12][13][14][15] lead to physically correct solid-particle motions [15,24,25]. Further details of these methods are discussed in Wen et al's review article [26].…”

Section: Introductionmentioning

confidence: 99%

Issues associated with Galilean invariance on a moving solid boundary in the lattice Boltzmann method

et al. 2017

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In lattice Boltzmann simulations involving moving solid boundaries, the momentum exchange between the solid and fluid phases was recently found to be not fully consistent with the principle of local Galilean invariance (GI) when the bounce-back schemes (BBS) and the momentum exchange method (MEM) are used. In the past, this inconsistency was resolved by introducing modified MEM schemes so that the overall moving-boundary algorithm could be more consistent with GI. However, in this paper we argue that the true origin of this violation of Galilean invariance (VGI) in the presence of a moving solid-fluid interface is due to the BBS itself, as the VGI error not only exists in the hydrodynamic force acting on the solid phase, but also in the boundary force exerted on the fluid phase, according to Newton's Third Law. The latter, however, has so far gone unnoticed in previously proposed modified MEM schemes. Based on this argument, we conclude that the previous modifications to the momentum exchange method are incomplete solutions to the VGI error in the lattice Boltzmann method (LBM). An implicit remedy to the VGI error in the LBM and its limitation is then revealed. To address the VGI error for a case when this implicit remedy does not exist, a bounce-back scheme based on coordinate transformation is proposed. Numerical tests in both laminar and turbulent flows show that the proposed scheme can effectively eliminate the errors associated with the usual bounce-back implementations on a no-slip solid boundary, and it can maintain an accurate momentum exchange calculation with minimal computational overhead.

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“…Then, Equation (36) should be modified for the calculation of the actual hydrodynamic force. As illuminated in previous works, 14,25‐29 the hydrodynamic force exerted on the bounce‐back point on the deformable solid related to the lattice link h should be expressed as

{bold-italicf}_{hydro}^{h} = false({bold-italice}_{h} - {bold-italicv}_{w} false) f_{h} false(x_{s}, t false) - false({bold-italice}_{\overset{h}{true}} - {bold-italicv}_{w} false) f_{\overset{h}{true}} false(x_{f 1}, t false) - 2 ρ_{f 0} ω_{h} {bold-italice}_{h} .

…”

Section: Fluid‐solid Coupling Algorithm In the Lbmpmmentioning

confidence: 98%

Coupling lattice Boltzmann and material point method for fluid‐solid interaction problems involving massive deformation

Liu

Zhang

et al. 2020

Numerical Meth Engineering

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This paper presents a coupling lattice Boltzmann and material point method (LBMPM) for fluid‐solid interaction problems involving massive deformation. The convected particle domain interpolation‐based material point method is adopted to solve the structure responses due to the particularly advantage on dynamic massive deformation simulations and the lattice Boltzmann method is utilized for its reliability and simplicity to simulate the complex fluid flow. The coupling strategy for these two methods is based on the consistent conditions with respect to displacement, velocity, and force, respectively, on the interface between fluid and solid parts, including the unified interpolation bounce‐back scheme for curved boundaries, the Galilean invariant momentum exchange method for hydrodynamic forces, the force imposing strategy particularly for massive deformation, and the refilling algorithm for moving boundaries. There is no remeshing operation needed in the proposed LBMPM for both solid and fluid parts even when solid massive deformation and fluid complex flow are considered. Three representative numerical examples are carried out and the simulation results demonstrate that the proposed LBMPM is capable of simulate complex bidirectional fluid‐solid interaction processes with the superiority for the problems involving solid dynamic large deformation behaviors and complex fluid flow.

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Hydrodynamic Force Evaluation by Momentum Exchange Method in Lattice Boltzmann Simulations

Cited by 27 publications

References 97 publications

A pseudopotential multiphase lattice Boltzmann model based on high-order difference

A pseudopotential multiphase lattice Boltzmann model based on high-order difference

Issues associated with Galilean invariance on a moving solid boundary in the lattice Boltzmann method

Coupling lattice Boltzmann and material point method for fluid‐solid interaction problems involving massive deformation

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