HYBRID FINITE-DIFFERENCE THERMAL LATTICE BOLTZMANN EQUATION

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A 3D incompressible thermal lattice Boltzmann model and its application to simulate natural convection in a cubic cavity (2004, background): “A good coverage of the literature review about the thermal LBM is given by Lallemand and Luo [4].”
Lattice Boltzmann methods for single-phase and solid-liquid phase-change heat transfer in porous media: A review (2018, methodology): “ been developed [7,85,87]: the 27 multispeed approach [135, 136, 137], the double-distribution-function (DDF) approach [138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148], and the hybrid approach [149, 150, 151, 152]. The multispeed approach was first proposed by Alexander et al. [136], in which”
Lattice Boltzmann methods for multiphase flow and phase-change heat transfer (2015, methodology): “Similar to the flow simulation in the DDF LB approach, in the hybrid approach the LB flow simulation is also separated from the solution of the temperature field, which is usually solved with conventional numerical methods, such as the finite-difference or finite-volume method [51, 104, 111, 212-216”
Viscous flow computations with the method of lattice Boltzmann equation (2003, background): “[144–146] pointed out that the origin of the TLBE (energy-conserving) models is due to the algebraic coupling of the viscous mode and the energy mode of the linearized system.”