A Critical Review of Forcing Schemes in Lattice Boltzmann Method: 1993–2019

Bawazeer, Saleh A.; Baakeem, Saleh S.; Mohamad, A. A.

doi:10.1007/s11831-021-09535-4

Cited by 18 publications

(7 citation statements)

References 28 publications

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“…The LBM is derived from the Boltzmann transport equation after being discretized in velocity space using a finite velocity set e i [54][55][56][57].…”

Section: Lattice Boltzmann Methodsmentioning

confidence: 99%

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Integrating a Stabilized Radial Basis Function Method with Lattice Boltzmann Method

2022

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The lattice Boltzmann method (LBM) has two key steps: collision and streaming. In a conventional LBM, the streaming is exact, where each distribution function is perfectly shifted to the neighbor node on the uniform mesh arrangement. This advantage may curtail the applicability of the method to problems with complex geometries. To overcome this issue, a high-order meshless interpolation-based approach is proposed to handle the streaming step. Owing to its high accuracy, the radial basis function (RBF) is one of the popular methods used for interpolation. In general, RBF-based approaches suffer from some stability issues, where their stability strongly depends on the shape parameter of the RBF. In the current work, a stabilized RBF approach is used to handle the streaming. The stabilized RBF approach has a weak dependency on the shape parameter, which improves the stability of the method and reduces the dependency of the shape parameter. Both the stabilized RBF method and the streaming of the LBM are used for solving three benchmark problems. The results of the stabilized method and the perfect streaming LBM are compared with analytical solutions or published results. Excellent agreements are observed, with a little advantage for the stabilized approach. Additionally, the computational cost is compared, where a marginal difference is observed in the favor of the streaming of the LBM. In conclusion, one could report that the stabilized method is a viable alternative to the streaming of the LBM in handling both simple and complex geometries.

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“…The LBM is derived from the Boltzmann transport equation after being discretized in velocity space using a finite velocity set e i [54][55][56][57].…”

Section: Lattice Boltzmann Methodsmentioning

confidence: 99%

“…Many approaches have been followed in the literature to discretize Equation (1). In the original LBM approach, the Lagrangian discretization is selected for the left-hand side [54][55][56][57].…”

Section: Lattice Boltzmann Methodsmentioning

confidence: 99%

Integrating a Stabilized Radial Basis Function Method with Lattice Boltzmann Method

2022

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“…This review does not aim to revise all existing forcing schemes. Instead, we present two popular methods, the Guo [239] and the Shan-Chen [240] forcing schemes, and refer to [241] for other schemes.…”

Section: Including External Forcesmentioning

confidence: 99%

“…There is a whole range of other forcing schemes that are also equivalent up to O(u 2 ) [241]. For IPMF applications, any second-order accurate forcing scheme is usually appropriate.…”

Section: Including External Forcesmentioning

confidence: 99%

Lattice-Boltzmann Modelling for Inertial Particle Microfluidics Applications — A Tutorial Review

Owen

Kechagidis

Bazaz

et al. 2023

Preprint

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Inertial particle microfluidics (IPMF) is an emerging technology for the manipulation and separation of microparticles and biological cells. Since the flow physics of IPMF is complex and experimental studies are often time-consuming or costly, computer simulations can offer complementary insights. In this tutorial review, we provide a guide for researchers who are exploring the potential of the lattice-Boltzmann (LB) method for simulating IPMF applications. We first review the existing literature to establish the state of the art of LB-based IPMF modelling. After summarising the physics of IPMF, we then present related methods used in LB models for IPMF and show several case studies of LB simulations for a range of IPMF scenarios. Finally, we conclude with an outlook and several proposed research directions.

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“…Although the treatment of body force is rather straightforward in both hydrodynamic equations and the Boltzmann equation, it remains a non-trivial and sometimes even controversial topic for the LBM after a substantial amount of effort and literally a dozen proposed schemes (Mohamad & Kuzmin 2010; Bawazeer, Baakeem & Mohamad 2021). The difficulty can be arguably attributed to the fact that the LBM was developed from beginning as a discrete kinetic model that was tailored a posteriori to exhibit Navier–Stokes–Fourier thermohydrodynamics at the macroscopic level.…”

Section: Introductionmentioning

confidence: 99%

Body-force modelling in thermal compressible flows with the lattice Boltzmann method

Li,

Shan

2023

J. Fluid Mech.

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Body-force modelling in the lattice Boltzmann method (LBM) has been studied extensively in the incompressible limit but rarely discussed for thermal compressible flows. Here we present a systematic approach of incorporating body force in the LBM which is valid for thermal compressible and non-equilibrium flows. In particular, a LBM forcing scheme accurate for the energy equation with second-order time accuracy is given. New and essential in this scheme is the third-moment contribution of the force term. It is shown via Chapman–Enskog analysis that the absence of this contribution causes an erroneous heat flux quadratic in Mach number and linear in temperature variation. The theoretical findings are verified and the necessity of the third-moment contribution is demonstrated by numerical simulations.

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A Critical Review of Forcing Schemes in Lattice Boltzmann Method: 1993–2019

Cited by 18 publications

References 28 publications

Integrating a Stabilized Radial Basis Function Method with Lattice Boltzmann Method

Integrating a Stabilized Radial Basis Function Method with Lattice Boltzmann Method

Lattice-Boltzmann Modelling for Inertial Particle Microfluidics Applications — A Tutorial Review

Body-force modelling in thermal compressible flows with the lattice Boltzmann method

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