Hybrid Method of Lattice Boltzmann Equations to Model Thermogravitational Flows

A hybrid mathematical model has been developed in which the flow field of a viscous incompressible medium is calculated by the method of lattice Boltzmann equations using the Bhatnagar–Gross–Krook approximation and a two-dimensional nine-velocity scheme, and free convective heat transfer is calculated by the finite difference method. The formulated approach to solving thermogravitational-convection problems has been verified on numerical and experimental data of other researchers. From a comparative analysis, it has been established that the computational efficiency of the hybrid mathematical model is 50 times higher than that of the traditional approach, which is based on the finite difference method and transformed "vorticity–stream function" variables.