AN IMPROVED THERMAL LATTICE BOLTZMANN MODEL FOR FLOWS WITHOUT VISCOUS HEAT DISSIPATION AND COMPRESSION WORK

Abstract

An improved lattice Boltzmann model is proposed for thermal flows in which the viscous heat dissipation and compression work by the pressure can be neglected. In the improved model, the whole complicated gradient term in the internal energy density distribution function model is correctly discarded by modifying the velocity moments' condition. The corresponding macroscopic energy equation is exactly derived through Chapman–Enskog expansion. In particular, based on the improved thermal model, a double-distribution-function lattice BGK model is developed for two-dimensional Boussinesq flow, which is a typical flow with negligible viscous heat dissipation and compression work. A two-dimensional plane flow and the natural convection of air in a square cavity with various Rayleigh numbers are simulated by using the double-distribution-function lattice BGK model. It is found that there is excellent agreement between the present results with the analytical or benchmark solutions.