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  • Title: Thermal lattice Boltzmann equation for low Mach number flows: decoupling model.
    Author: Guo Z, Zheng C, Shi B, Zhao TS.
    Journal: Phys Rev E Stat Nonlin Soft Matter Phys; 2007 Mar; 75(3 Pt 2):036704. PubMed ID: 17500823.
    Abstract:
    A lattice Boltzmann model is proposed for solving low Mach number thermal flows with viscous dissipation and compression work in the double-distribution-function framework. A distribution function representing the total energy is defined based on a single velocity distribution function, and its evolution equation is derived from the continuous Boltzmann equation. A lattice Boltzmann equation model with clear physics and a simple structure is then obtained from a kinetic model for the decoupled hydrodynamic and energy equations. The model is tested by simulating a thermal Poiseuille flow and natural convection in a square cavity, and it is found that the numerical results agree well with the analytical solutions and/or the data reported in previous studies.
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