Hybrid Lattice Boltzmann Equation Method in Problems of Coupled Heat Transfer

A hybrid (LB–FD) mathematical model has been constructed to investigate thermogravitational convection in closed rectangular cavities limited on one side by a heat-conducting wall of finite thickness. Within the framework of the formulated approach, the hydrodynamics is simulated by the lattice Boltzmann equation method using a Bhatnagar–Gross–Krook approximation and a two-dimensional nine-velocity scheme, and energy and heat conduction equations are solved by the method of finite differences. Numerical simulation has been conducted in varying the Rayleigh number, thickness, and relative heat conductivity of a wall. It has been established that the developed hybrid model provides an adequate reproduction of local and average characteristics of coupled heat transfer. The computation speed of the LB–FD model is 10 times higher compared to the approach based on solving Navier–Stokes equations in transformed “vorticity–flow function” variables.