Modeling incompressible thermal flows using a central-moment-based lattice Boltzmann method

In this paper, a central-moment-based lattice Boltzmann (CLB) method for incompressible thermal flows is proposed. In the method, the incompressible Navier-Stokes equations and the convection-diffusion equation for the temperature field are sloved separately by two different CLB equations. Through the Chapman-Enskog analysis, the macroscopic governing equations for incompressible thermal flows can be reproduced. For the flow field, the tedious implementation for CLB method is simplified by using the shift matrix with a simplified central-moment set, and the consistent forcing scheme is adopted to incorporate forcing effects. Compared with several D2Q5 multiple-relaxation-time (MRT) lattice Boltzmann methods for the temperature equation, the proposed method is shown to be better Galilean invariant through measuring the thermal diffusivities on a moving reference frame. Thus a higher Mach number can be used for convection flows, which decreases the computational load significantly. Numerical simulations for several typical problems confirm the accuracy, efficiency, and stability of the present method. The grid convergence tests indicate that the proposed CLB method for incompressible thermal flows is of second-order accuracy in space

A modified lattice Bhatnagar-Gross-Krook model for convection heat transfer in porous media

The lattice Bhatnagar-Gross-Krook (LBGK) model has become the most popular one in the lattice Boltzmann method for simulating the convection heat transfer in porous media. However, the LBGK model generally suffers from numerical instability at low fluid viscosities and effective thermal diffusivities. In this paper, a modified LBGK model is developed for incompressible thermal flows in porous media at the representative elementary volume scale, in which the shear rate and temperature gradient are incorporated into the equilibrium distribution functions. With two additional parameters, the relaxation times in the collision process can be fixed at a proper value invariable to the viscosity and the effective thermal diffusivity. In addition, by constructing a modified equilibrium distribution function and a source term in the evolution equation of temperature field, the present model can recover the macroscopic equations correctly through the Chapman-Enskog analysis, which is another key point different from previous LBGK models. Several benchmark problems are simulated to validate the present model with the proposed local computing scheme for the shear rate and temperature gradient, and the numerical results agree well with analytical solutions and/or those well-documented data in previous studies. It is also shown that the present model and the computational schemes for the gradient operators have a second-order accuracy in space, and better numerical stability of the present modified LBGK model than previous LBGK models is demonstrated.Comment: 38pages,50figure

A lattice Boltzmann model for natural convection in cavities

We study a multiple relaxation time lattice Boltzmann model for natural convection with moment–based boundary conditions. The unknown primary variables of the algorithm at a boundary are found by imposing conditions directly upon hydrodynamic moments, which are then translated into conditions for the discrete velocity distribution functions. The method is formulated so that it is consistent with the second–order implementation of the discrete velocity Boltzmann equations for fluid flow and temperature. Natural convection in square cavities is studied for Rayleigh numbers ranging from 103 to 106. An excellent agreement with benchmark data is observed and the flow fields are shown to converge with second order accuracy

Natural convection with mixed insulating and conducting boundary conditions: low and high Rayleigh numbers regimes

We investigate the stability and dynamics of natural convection in two dimensions, subject to inhomogeneous boundary conditions. In particular, we consider a Rayleigh-B\`enard (RB) cell, where the horizontal top boundary contains a periodic sequence of alternating thermal insulating and conducting patches, and we study the effects of the heterogeneous pattern on the global heat exchange, both at low and high Rayleigh numbers. At low Rayleigh numbers, we determine numerically the transition from a regime characterized by the presence of small convective cells localized at the inhomogeneous boundary to the onset of bulk convective rolls spanning the entire domain. Such a transition is also controlled analytically in the limit when the boundary pattern length is small compared with the cell vertical size. At higher Rayleigh number, we use numerical simulations based on a lattice Boltzmann method to assess the impact of boundary inhomogeneities on the fully turbulent regime up to $Ra \sim 10^{10}$

Validation and application of the lattice Boltzmann algorithm for a turbulent immiscible Rayleigh-Taylor system

We develop a multicomponent lattice Boltzmann (LB) model for the 2D Rayleigh--Taylor turbulence with a Shan-Chen pseudopotential implemented on GPUs. In the immiscible case this method is able to accurately overcome the inherent numerical complexity caused by the complicated structure of the interface that appears in the fully developed turbulent regime. Accuracy of the LB model is tested both for early and late stages of instability. For the developed turbulent motion we analyze the balance between different terms describing variations of the kinetic and potential energies. Then, we analyze the role of interface in the energy balance, and also the effects of the vorticity induced by the interface in the energy dissipation. Statistical properties are compared for miscible and immiscible flows. Our results can also be considered as a first validation step to extend the application of LB model to 3D immiscible Rayleigh-Taylor turbulence.Comment: 14 pages, 6 figures. arXiv admin note: substantial text overlap with arXiv:2009.0005