Improved axisymmetric lattice Boltzmann scheme

Owing to its conceptual simplicity and computational efficiency, the pseudopotential multiphase lattice Boltzmann (LB) model has attracted significant attention since its emergence. In this work, we aim to extend the pseudopotential LB model to simulate multiphase flows at large density ratio and relatively high Reynolds number. First, based on our recent work [Q. Li, K. H. Luo, and X. J. Li, Phys. Rev. E 86, 016709 (2012)], an improved forcing scheme is proposed for the multiple-relaxation-time pseudopotential LB model in order to achieve thermodynamic consistency and large density ratio in the model. Next, through investigating the effects of the parameter a in the Carnahan-Starling equation of state, we find that the interface thickness is approximately proportional to 1/ √ a. Using a smaller a will lead to a wider interface thickness, which can reduce the spurious currents and enhance the numerical stability of the pseudopotential model at large density ratio. Furthermore, it is found that a lower liquid viscosity can be gained in the pseudopotential model by increasing the kinematic viscosity ratio between the vapor and liquid phases. The improved pseudopotential LB model is numerically validated via the simulations of stationary droplet and droplet oscillation. Using the improved model as well as the above treatments, numerical simulations of droplet splashing on a thin liquid film are conducted at a density ratio in excess of 500 with Reynolds numbers ranging from 40 to 1000. The dynamics of droplet splashing is correctly reproduced and the predicted spread radius is found to obey the power law reported in the literature.

show abstract

“…With the MRT collision operator [37,38], the evolution equation of the density distribution function can be written as [28,32,39] …”

Section: Mrt Pseudopotential Lb Modelmentioning

confidence: 99%

Lattice Boltzmann modeling of multiphase flows at large density ratio with an improved pseudopotential model

2013

Self Cite

View full text Add to dashboard Cite

show abstract

“…In recent years several implementations of the axisymmetric LBM for single-phase systems have been proposed [4][5][6][7][8][9], while, in comparison, relatively little attention has been devoted to the case of the multiphase flow [10,11].…”

Section: Introductionmentioning

confidence: 99%

Axisymmetric multiphase lattice Boltzmann method

et al. 2013

View full text Add to dashboard Cite

A lattice Boltzmann method for axisymmetric multiphase flows is presented and validated. The method is capable of accurately modeling flows with variable density. We develop the classic Shan-Chen multiphase model [Phys. Rev. E 47, 1815(1993] for axisymmetric flows. The model can be used to efficiently simulate single and multiphase flows. The convergence to the axisymmetric Navier-Stokes equations is demonstrated analytically by means of a Chapmann-Enskog expansion and numerically through several test cases. In particular, the model is benchmarked for its accuracy in reproducing the dynamics of the oscillations of an axially symmetric droplet and on the capillary breakup of a viscous liquid thread. Very good quantitative agreement between the numerical solutions and the analytical results is observed.

show abstract

“…The single-relaxationtime lattice Boltzmann methods are limited to isotropic diffusion. Multiple-relaxation-time lattice Boltzmann methods offer a more suitable framework for simulating anisotropic diffusion, and are more easily presentable in the momentum space [Lallemand and Lou, 2000;Li et al, 2010]. The distributions can be transformed to moments using the following linear operation:…”

Section: The Lattice Boltzmann Methodsmentioning

confidence: 99%

Do Current Lattice Boltzmann Methods for Diffusion and Advection-Diffusion Equations Respect Maximum Principle and the Non-Negative Constraint?

Karimi

Nakshatrala

2016

Commun. Comput. Phys.

View full text Add to dashboard Cite

Abstract. The lattice Boltzmann method (LBM) has established itself as a valid numerical method in computational fluid dynamics. Recently, multiple-relaxation-time LBM has been proposed to simulate anisotropic advection-diffusion processes. The governing differential equations of advective-diffusive systems are known to satisfy maximum principles, comparison principles, the non-negative constraint, and the decay property. In this paper, it will be shown that current single-and multiple-relaxation-time lattice Boltzmann methods fail to preserve these mathematical properties for transient diffusion and advection-diffusion equations. It will also be shown that the discretization of Dirichlet boundary conditions will affect the performance of lattice Boltzmann methods in meeting these mathematical principles. A new way of discretizing the Dirichlet boundary conditions is also proposed. Several benchmark problems have been solved to illustrate the performance of lattice Boltzmann methods and the effect of discretization of boundary conditions with respect to the aforementioned mathematical properties.

show abstract

Improved axisymmetric lattice Boltzmann scheme

Cited by 117 publications

References 61 publications

Lattice Boltzmann modeling of multiphase flows at large density ratio with an improved pseudopotential model

Lattice Boltzmann modeling of multiphase flows at large density ratio with an improved pseudopotential model

Axisymmetric multiphase lattice Boltzmann method

Do Current Lattice Boltzmann Methods for Diffusion and Advection-Diffusion Equations Respect Maximum Principle and the Non-Negative Constraint?

Contact Info

Product

Resources

About