The development of thermal lattice Boltzmann models in incompressible limit
Keywords:Distribution function, Thermal lattice Boltzmann, Porous Couette flow, Lid-driven cavity flow,
AbstractIn this paper, an incompressible two-dimensional (2-D) and three-dimensional (3-D) thermohydrodynamics for the
lattice Boltzmann scheme are developed. The basic idea is to solve the velocity field and the temperature field using
two different distribution functions. A derivation of the lattice Boltzmann scheme from the continuous Boltzmann
equation for 2-D is discussed in detail. By using the same procedure as in the derivation of the discretised density
distribution function, we found that new lattice of four-velocity (2-D) and eight-velocity (3-D) models for internal energy
density distribution function can be developed where the viscous and compressive heating effects are negligible.
These models are validated by the numerical simulation of the 2-D porous plate Couette flow problem where the
analytical solution exists and the natural convection flows in a cubic cavity.
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