Hybrid method of lattice boltzmann equations to model thermogravitational flows

A hybrid mathematical model has been developed in which the fl ow fi eld 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 fi nite difference method. The formulated approach to solving thermogravitational-convection problems has been verifi ed on numerical and experimental data of other researchers. From a comparative analysis, it has been established that the computational effi ciency of the hybrid mathematical model is 50 times higher than that of the traditional approach, which is based on the fi nite difference method and transformed "vorticity–stream function" variables.
A hybrid mathematical model has been developed in which the fl ow fi eld 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 fi nite difference method. The formulated approach to solving thermogravitational-convection problems has been verifi ed on numerical and experimental data of other researchers. From a comparative analysis, it has been established that the computational effi ciency of the hybrid mathematical model is 50 times higher than that of the traditional approach, which is based on the fi nite difference method and transformed "vorticity–stream function" variables.
Author:  A. É. Ni
Keywords:  method of lattice Boltzmann equations, fi nite difference method, Bhatnagar–Gross–Krook approximation
Page:  415-422