Lattice Boltzmann simulations of thermal flows beyond the Boussinesq and ideal-gas approximations

Abstract

In this work, the recent lattice Boltzmann model with self-tuning equation of state (EOS) [R. Huang et al., J. Comput. Phys. 392, 227 (2019)] is improved in three aspects to simulate the thermal flows beyond the Boussinesq and ideal-gas approximations. First, an improved scheme is proposed to eliminate the additional cubic terms of velocity, which can significantly improve the numerical accuracy. Second, a local scheme is proposed to calculate the density gradient instead of the conventional finite-difference scheme. Third, a scaling factor is introduced into the lattice sound speed, which can be adjusted to effectively enhance numerical stability. The thermal Couette flow of a nonattracting rigid-sphere fluid, which is described by the Carnahan-Starling EOS, is first simulated, and the better performance of the present improvements on the numerical accuracy and stability is demonstrated. As a further application, the turbulent Rayleigh-Bénard convection in a supercritical fluid slightly above its critical point, which is described by the van der Waals EOS, is successfully simulated by the present lattice Boltzmann model. The piston effect of the supercritical fluid is successfully captured, which induces a fast and homogeneous increase of the temperature in the bulk region, and the time evolution from the initiation of heating to the final turbulent state is analyzed in detail and divided into five stages.

Mesoscopic Lattice Boltzmann Modeling of the Liquid-Vapor Phase Transition

“…Therefore, thermodynamic consistency naturally emerges from our mesoscopic LB model developed in accordance with the kinetic model. Note that there exist some additional cubic terms of velocity in recovering the viscous stress tensor [27,28], which are ignored with the low Mach number condition and can also be eliminated by trivial modifications [23,29]. Moreover, the present LB model shows satisfactory numerical stability due to the separate incorporations of the short-and long-range molecular interactions and the introduction of an innovative, simple yet effective, total kinetic energy DF.…”

“…This boundary condition is treated by the improved nonequilibrium-extrapolation scheme [31]. Meanwhile, eliminating the additional cubic terms of velocity is also plugged into the LB model [29]. Before simulating liquid-vapor phase transition, an equilibrium droplet in periodic domain is considered.…”

Surface thermodynamics and wetting condition in the multiphase lattice Boltzmann model with self-tuning equation of state

“…For the sake of completeness, the recent multiphase LB model with a self-tuning EOS is briefly introduced in this section, and the reader is referred to previous works (Huang, Wu & Adams 2019a;Huang et al 2019c;Huang, Lan & Li 2020) for more details. The LB equation for the density distribution function f i (x, t) can be written as (Huang et al 2019a)…”

“…the right-hand side of (2.1 b )) (Huang et al. 2020) where , and are , and matrices Considering and , in (A3) can be evaluated with the help of as follows: where is locally calculated by (2.10). The non-zero elements in the matrix are determined by (Huang et al.…”

“…The non-zero elements in the matrix are determined by (Huang et al. 2020) where is a matrix and the coefficients , , , , , , , and are The non-zero elements in the matrix are determined by (Huang et al. 2020) where the coefficients , and are The non-zero elements in the matrix are determined by (Huang et al.…”