A novel thermal lattice Boltzmann model with heat source and its application in incompressible flow

Abstract

In this paper, the source term of energy distribution in double distribution function approach is analysed in detail and a new discrete model is proposed to eliminate the error terms in previous models. The newly proposed model contains two coupling terms, i.e. a velocity-source coupling term and a temperature-force coupling term. The velocity-source coupling term is related to the transport of source which affects the accuracy of simulations of convection, chemical reaction and so on. The temperature-force coupling term is related to the inner product of force and temperature gradient which affects the accuracy of simulations of boundary layer and the edge of plumes in convection. We extended two new heuristic treatments to handle the adiabatic and isothermal boundary conditions. Their efficiency and accuracy are analyzed theoretically and proved by some numerical validations. Finally, we simulated natural convection flows with compression work and viscous dissipation over a wide range of Eckert number using the present model and obtained a scaling law between average Nusselt number and Eckert number.