A Thermal Lattice Boltzmann Model for Flows with Viscous Heat Dissipation
Hao-Chueh Mai; Kuen-Hau Lin, Cheng-Hsiu Yang and Chao-An Lin;

Source CMES: Computer Modeling in Engineering & Sciences, Vol. 61, No. 1, pp. 45-62, 2010
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Keywords Thermal lattice Boltzmann model, viscous heat dissipation, BGK model, natural convection, second order accuracy.
Abstract A thermal BGK lattice Boltzmann model for flows with viscous heat dissipation is proposed. In this model, the temperature is solved by a separate thermal distribution function, where the equilibrium distribution function is similar to its hydrodynamic counterpart, except that the leading quantity is temperature. The viscous dissipation rate is obtained by computing the second-order moments of non-equilibrium distribution function, which avoids the discretization of the complex gradient term, and can be easily implemented. The proposed thermal lattice Boltzmann model is scrutinized by computing two-dimensional thermal Poiseuille flow, thermal Couette flow, natural convection in a square cavity, and three-dimensional thermal Poiseuille flow in a square duct. Numerical simulations indicate that the second order accurate LBM scheme is not degraded by the present thermal BGK lattice Boltzmann model.
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