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)]JCTPAH0021-999110.1016/j.jcp.2019.04.044 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.
Highlights
The lattice Boltzmann (LB) method, developed over the past three decades, has been exploited to simulate various flow problems, including the fluid-structure interactions [1,2], porous media flows [3,4], multiphase flows [5,6,7], phase change problems [8,9,10], etc
The turbulent Rayleigh-Bénard convection in a supercritical fluid slightly above its critical point, which is described by the van der Waals equation of state (EOS), is successfully simulated by the present lattice Boltzmann model
An improved scheme is proposed to eliminate the additional cubic terms of velocity, a local scheme is proposed to calculate the density gradient, and a scaling factor is introduced into the lattice sound speed
Summary
The lattice Boltzmann (LB) method, developed over the past three decades, has been exploited to simulate various flow problems, including the fluid-structure interactions [1,2], porous media flows [3,4], multiphase flows [5,6,7], phase change problems [8,9,10], etc. Starting with the Boltzmann equation in kinetic theory, some DDF LB models [24,25,26] are developed in an a priori manner for the simulation of thermal flows, in which the viscous dissipation and compression work can be naturally incorporated In these thermal LB models [21,22,23,24,25,26], the recovered equation of state (EOS) is decoupled from the temperature and can be generally written as p = ρcs with cs denoting the constant lattice sound speed. The class (IV) model [17] recovers a self-tuning EOS p = cs2[(2 + α1)ρ + β1η], which can be arbitrarily specified in practice As a result, this model can handle the general thermal flows beyond both the Boussinesq and ideal-gas approximations.
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