An improved multiphase lattice Boltzmann flux solver for the simulation of incompressible flow with large density ratio and complex interface

Yang, Liuming; Chen, Shu; Жен, Чен; Hou, Guoxiang; Wang, Yan

doi:10.1063/5.0038617

Cited by 28 publications

(12 citation statements)

References 51 publications

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“…Aiming to unify the different computational frameworks for velocity and phase fields, an interfacial lattice Boltzmann flux solver (ILBFS) [23] was proposed to solve the Cahn-Hilliard equation. Based on ILBFS, a simplified MLBFS with slight simplification in interface fluxes [24] and an improved MLBFS (IMLBFS) [25] based on the original phase-field-based multiphase lattice Boltzmann model (MLBM) [26] were proposed.…”

Section: Introductionmentioning

confidence: 99%

“…The reason for the good numerical stability of the original MLBFS was thought to be using the lattice Boltzmann model [21]. IMLBFS is believed to be more stable than the original MLBFS because it is derived from the multiphase lattice Boltzmann model and thus has a more robust physical basis [25]. The reason for the good numerical stability of SMLBM is recognized as that SMLBM inherits the good stability feature of the reconstruction strategy [20].…”

Section: Introductionmentioning

confidence: 99%

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General mechanisms for stabilizing weakly compressible multiphase models and their applications

Adams

2023

Preprint

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The present paper analyzes three representative weakly compressible multiphase models. It is found that these models contain some identical numerical dissipation terms, pressure diffusion, and bulk viscosity terms. Numerical investigations show that these identical numerical dissipation terms interpret general mechanisms for stabilizing computations. The generality of mechanisms is reflected in (a) they are likely to present in many weakly compressible multiphase models and (b) they represent interpretable physical mechanisms. Based on those general mechanisms, many weakly compressible multiphase models can be incorporated into a general theoretical framework. And a general weakly compressible solver for multiphase flows (GWCS-MF) is proposed. It is derived from standard governing equations and can easily be applied to nonuniform meshes. Detailed numerical tests demonstrate that it can achieve good numerical stability and accuracy for challenging conditions (inviscid fluids, large density ratios, high Weber numbers, and high Reynolds numbers) and can simulate complex interface evolution well. These good performances exhibit the advantages of GWCS-MF and further validate those general mechanisms.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

General mechanisms for stabilizing weakly compressible multiphase models and their applications

Adams

2023

Preprint

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“…These deficiencies make it difficult for standard LBM or LLBM to simulate acoustic wave propagation. To solve these deficiencies, Shu et al proposed the lattice Boltzmann flux solver (LBFS) employing the finite volume method to calculate the flux at an interface [ 26 , 27 , 28 , 29 , 30 ]. Zhan et al further developed a linearized lattice Boltzmann flux solver (LLBFS) suitable for acoustic propagation simulation [ 31 ], wherein the solution of the interface satisfies the lattice Boltzmann equation; this is more in line with physical laws, and the calculation load is comparable to the traditional flux scheme.…”

Section: Introductionmentioning

confidence: 99%

A Simplified Linearized Lattice Boltzmann Method for Acoustic Propagation Simulation

Song

Chen

Cao

et al. 2022

Entropy

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A simplified linearized lattice Boltzmann method (SLLBM) suitable for the simulation of acoustic waves propagation in fluids was proposed herein. Through Chapman–Enskog expansion analysis, the linearized lattice Boltzmann equation (LLBE) was first recovered to linearized macroscopic equations. Then, using the fractional-step calculation technique, the solution of these linearized equations was divided into two steps: a predictor step and corrector step. Next, the evolution of the perturbation distribution function was transformed into the evolution of the perturbation equilibrium distribution function using second-order interpolation approximation of the latter at other positions and times to represent the nonequilibrium part of the former; additionally, the calculation formulas of SLLBM were deduced. SLLBM inherits the advantages of the linearized lattice Boltzmann method (LLBM), calculating acoustic disturbance and the mean flow separately so that macroscopic variables of the mean flow do not affect the calculation of acoustic disturbance. At the same time, it has other advantages: the calculation process is simpler, and the cost of computing memory is reduced. In addition, to simulate the acoustic scattering problem caused by the acoustic waves encountering objects, the immersed boundary method (IBM) and SLLBM were further combined so that the method can simulate the influence of complex geometries. Several cases were used to validate the feasibility of SLLBM for simulation of acoustic wave propagation under the mean flow.

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“…In this article, the initial distribution function is given from the first-order Chapman-Enskog (C-E) expansion. [23][24][25][26] It is indeed the distribution function truncated to the NS level. After some transformation, this distribution function can be expressed explicitly as the function of conservative variables and their derivatives.…”

Section: Introductionmentioning

confidence: 99%

“…In this article, the initial distribution function is given from the first‐order Chapman–Enskog (C‐E) expansion 23–26 . It is indeed the distribution function truncated to the NS level.…”

Section: Introductionmentioning

confidence: 99%

A novel gas kinetic flux solver for simulation of continuum and slip flows

Yuan

Yang

Chen

et al. 2021

Numerical Methods in Fluids

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In this work, a novel gas kinetic flux solver (GKFS) is presented for simulation of compressible and incompressible flows in the continuum and slip regimes. The finite volume method is adopted to discretize the governing differential equations, and inviscid and viscous fluxes at the cell interface are evaluated simultaneously by the local solution to the Boltzmann equation. Different from the conventional GKFS, in which the local solution to the Boltzmann equation is divided into the equilibrium part and the nonequilibrium part and the nonequilibrium distribution function is approximated by the difference of equilibrium distribution functions at the cell interface and its surrounding points, the present solver evaluates the local solution by integrating the Boltzmann equation along the characteristic line. As a result, the local solution to the Boltzmann equation consists of the equilibrium distribution function at the cell interface and the initial distribution function at the surrounding points. In the present work, the initial distribution function is given from the first‐order Chapman–Enskog expansion. Finally, the distribution function at the cell interface is only relevant to the macroscopic variables and their spatial derivatives. Accordingly, the fluxes across the cell interface can be evaluated by the moments of the distribution function at the cell interface. Test results show that the present solver can provide accurate numerical predictions for flows in both continuum and slip regimes.

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An improved multiphase lattice Boltzmann flux solver for the simulation of incompressible flow with large density ratio and complex interface

Cited by 28 publications

References 51 publications

General mechanisms for stabilizing weakly compressible multiphase models and their applications

General mechanisms for stabilizing weakly compressible multiphase models and their applications

A Simplified Linearized Lattice Boltzmann Method for Acoustic Propagation Simulation

A novel gas kinetic flux solver for simulation of continuum and slip flows

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