Abstract
Cascaded or central-moment-based lattice Boltzmann method (CLBM) is a relatively recent development in the LBM community, which has better numerical stability and naturally achieves better Galilean invariance for a specified lattice compared with the classical single-relation-time (SRT) LBM. Recently, CLBM has been extended to simulate thermal flows based on the double-distribution-function (DDF) approach [L. Fei et al., Int. J. Heat Mass Transfer 120, 624 (2018)]. In this work, CLBM is further extended to simulate thermal flows involving complex thermal boundary conditions and/or a heat source. Particularly, a discrete source term in the central-moment space is proposed to include a heat source, and a general bounce-back scheme is employed to implement thermal boundary conditions. The numerical results for several canonical problems are in good agreement with the analytical solutions and/or numerical results in the literature, which verifies the present CLBM implementation for thermal flows.
Highlights
In the last three decades or so, the lattice Boltzmann method (LBM), which is a mesoscopic numerical method based on the kinetic theory, has been developed to be a widely used numerical method for solving various fluid flows and heat transfer problems [1, 2, 3, 4, 5, 6, 7]
In the BGK-LBM, all the distribution functions are relaxed to their local equilibrium states at an identical rate, where the relaxation rate is related to the kinematic viscosity
In the MRT-LBM, the distribution functions (DFs) is transformed into a raw moment space, where different raw moments of the DF can be relaxed at different relaxation rates to the local equilibrium raw moments
Summary
In the last three decades or so, the lattice Boltzmann method (LBM), which is a mesoscopic numerical method based on the kinetic theory, has been developed to be a widely used numerical method for solving various fluid flows and heat transfer problems [1, 2, 3, 4, 5, 6, 7]. The BGK-LBM is quite simple to implement and can simulate low Reynolds number flows, but it may have numerical instability at high Reynolds number or low-viscosity flows, as well as inaccuracy of implementing the boundary conditions [11, 12, 13, 14, 15] To overcome these difficulties, the multiple-relaxation-time (MRT) collision operator was proposed in the literature [11, 12]. The rest of the paper is structured as follows: In Section 2, a brief introduction for the DDF-based CLBM for incompressible thermal flows is given, followed by the implementation of a heat source and general bounce-back scheme for thermal boundary conditions. Where the gravitational acceleration vector g points to the negative direction of y-axis, β is the thermal expansion coefficient, T0 is the reference temperature, and Fv is an external body force
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