Abstract
In this paper, a thermal cascaded lattice Boltzmann method (TCLBM) is developed in combination with the double-distribution-function (DDF) approach on the standard D2Q9 lattice. A density distribution function relaxed by the cascaded scheme based on central moments is employed to solve the flow field, and a total energy distribution function relaxed by the BGK scheme is used to solve the temperature field. The two distribution functions are coupled naturally to provide a new TCLBM. In this method, the viscous heat dissipation and compression work are taken into account, the Prandtl number and specific-heat ratio are adjustable, and the external force is considered directly without the Boussinesq assumption. The TCLBM is validated by numerical experiments of the thermal Couette flow, low-Mach number shock tube problem, Rayleigh-Bénard convection, and natural convection in a square cavity with a large temperature difference. The simulation results agree well with the analytical solutions and/or results given by previous researchers.
Highlights
The lattice Boltzmann method (LBM), based on the kinetic theory, has achieved remarkable success as an alternative method to conventional computational fluid dynamics (CFD) for thermal flow and heat transfer applications during the past three decades [1,2,3,4,5,6,7,8,9]
The collision in the cascaded Lattice Boltzmann method (CLBM) is performed by relaxing central moments to their local equilibrium values separately, which is different from MRT LBM where the raw moments are relaxed
We developed a thermal cascaded lattice Boltzmann method (TCLBM) for low-Mach compressible thermal flows on standard lattices
Summary
The lattice Boltzmann method (LBM), based on the kinetic theory, has achieved remarkable success as an alternative method to conventional computational fluid dynamics (CFD) for thermal flow and heat transfer applications during the past three decades [1,2,3,4,5,6,7,8,9]. At each time step the collision is first locally executed and followed by streaming the post-collision distributions to their neighbors, or just exchanging the above procedure [12] Based on this algorithm, various collision operators can be adopted, such as the single-relaxation-time (SRT) or BGK operator [13], tworelaxation-time (TRT) operator [14,15], multiple-relaxation-time (MRT) operator [16,17], and entropic operator [18,19,20]. In 2012, Li et al [4] developed a coupling DDF thermal model which can simulate more general thermal flows, and the model was extended to three-dimensions by Feng et al [33] recently Inspired by these works, we construct a thermal cascaded lattice Boltzmann method (TCLBM) in the present work based on the DDF approach.
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