RESUMO

We propose alternative discretization schemes for improving the lattice Boltzmann pseudopotential model for incompressible multicomponent systems, with the purpose of modeling the flow of immiscible fluids with a large viscosity ratio. Compared to the original model of Shan-Chen [Phys. Rev. E 47, 1815 (1993)1063-651X10.1103/PhysRevE.47.1815], the present discretization schemes consider: (i) an explicit force term, (ii) a second-order discretization of the stream term, (iii) a moments-based model for the kinetic nonequilibrium distributions, and (iv) a high-order discretization of the spatial derivative terms. To verify the accuracy of the proposed model, the effects of varying the viscosity ratio as well as both fluid's viscosities on spurious currents and capillary number are investigated for the problems dealing with a static bubble, two-component Poiseuille flow, and immiscible fluid-fluid displacement. The resulting algorithm maintains the simplicity of the pseudopotential model while allowing an easy implementation for multicomponent systems. The results of the model herein proposed show improved control of the interface region and interfacial tension, relatively smaller magnitudes of spurious current values with increasing viscosity ratio, and also a significantly wider stability range with respect to the previously best results in the literature.

RESUMO

We propose isotropic finite differences for high-accuracy approximation of high-rank derivatives. These finite differences are based on direct application of lattice-Boltzmann stencils. The presented finite-difference expressions are valid in any dimension, particularly in two and three dimensions, and any lattice-Boltzmann stencil isotropic enough can be utilized. A theoretical basis for the proposed utilization of lattice-Boltzmann stencils in the approximation of high-rank derivatives is established. In particular, the isotropy and accuracy properties of the proposed approximations are derived directly from this basis. Furthermore, in this formal development, we extend the theory of Hermite polynomial tensors in the case of discrete spaces and present expressions for the discrete inner products between monomials and Hermite polynomial tensors. In addition, we prove an equivalency between two approaches for constructing lattice-Boltzmann stencils. For the numerical verification of the presented finite differences, we introduce 5th-, 6th-, and 8th-order two-dimensional lattice-Boltzmann stencils.

Assuntos

Algoritmos , Modelos Teóricos , Anisotropia , Simulação por Computador , Análise de Elementos Finitos

RESUMO

The thermodynamic consistency of kinetic models for non-ideal mixtures in non-isothermal conditions is investigated. A kinetic model is proposed that is suitable for deriving high-order lattice Boltzmann equations by an appropriate discretization of the velocity space, satisfying the Galilean invariance condition and free of spurious terms in the first moment equations.