Finite-difference lattice Boltzmann model with flux limiters for liquid-vapor systems

Abstract

In this paper we apply a finite difference lattice Boltzmann model to study the phase separation in a two-dimensional liquid-vapor system. Spurious numerical effects in macroscopic equations are discussed and an appropriate numerical scheme involving flux limiter techniques is proposed to minimize them and guarantee a better numerical stability at very low viscosity. The phase separation kinetics is investigated and we find evidence of two different growth regimes depending on the value of the fluid viscosity as well as on the liquid-vapor ratio.

FFT-LB Modeling of Thermal Liquid-Vapor System

“…Apart from the fields listed above, this versatile method is particularly promising in the area of multiphase systems [17,18,19,20,21,22,23]. This is partly owing to its intrinsic kinetic nature, which makes the inter-particle interactions (IPI) be incorporated easily and flexibly, and, in fact, the IPI is the underlying microscopic physical reason for phase separation and interfacial tension in multiphase systems.…”

“…Sofonea and Cristea et al [23,38] presented a finite difference LB (FDLB) approach and proposed two ways to eliminate the unwanted currents. In the first way, a high-accuracy numerical scheme, the flux limiter method is employed to calculate the convection term of the LB equation.…”

“…The aforementioned models have been successfully applied to a wide variety of multiphase and/or multicomponent flow problems, including drop breakup [25,26], drop collisions [27], wetting [28,29], contact line motion [30,31], chemically reactive fluids [32], phase separation and phase ordering phenomena [19,21,23,33], hydrodynamic instability [34,35], etc.…”

The Design and Application of English Online Learning System Based on Bs

“…Among them, the entropic LB method [16,17] tries tomake the scheme to follow the Htheorem; The FIX-UP method [16,18] is based on the standard BGK scheme, usesa third-order equilibrium distribution function and a selfadapting updating parameter to avoid negativeness of themass distribution function. Flux limiter techniques are used to enhance the stability of FDLB by Sofonea, et al [19].Adding minimal dissipation locally to improve the stability is also suggested by Brownlee, et al [20], but there suchan approach is not explicitly discussed. All the abovementioned attempts are for low Mach number flows.…”

“…But similar to previous LB models, the numerical stability problemremains one of the few blocks for its practical simulation to high Mach number flows. The stability problem of LBhas been addressed and attempted for some years [13][14][15][16][17][18][19][20][21][22][23]. Among them, the entropic LB method [16,17] tries tomake the scheme to follow the Htheorem; The FIX-UP method [16,18] is based on the standard BGK scheme, usesa third-order equilibrium distribution function and a selfadapting updating parameter to avoid negativeness of themass distribution function.…”