Discrete-Velocity Models and Lattice Boltzmann Methods for Convection-Radiation Problems

Discrete-velocity models and lattice Boltzmann methods are presented for solving convection-radiation effects in thermal fluid flows. The discrete-velocity equations are derived from the continuous Boltzmann equation with appropriate scaling suitable for incompressible flows. The radiative heat flux in the energy equation is obtained using the discrete-ordinates solution of the radiative transfer equation. This chapter is structured in two parts. In the first part we investigate the derivation of the discrete-velocity models and we perform an asymptotic analysis to show at the leading order, the macroscopic models are recovered from these discrete-velocity models. In this part we also formulate the lattice Boltzmann method for solving the convection-radiation problems. The second part of this chapter is devoted to the computational aspects of the considered models. Consistent boundary and initial conditions in the lattice Boltzmann models are also discussed in this part. Numerical results are presented for several test examples on coupled convectionradiation flows in two dimensional enclosures. Detailed simulation results at different flow and radiative regimes, as well as benchmark solutions, are also presented and discussed. The obtained results show that the developed models are competitive tools for convectionradiation problems.

Keywords: Discrete-velocity models, forced convection, heat transfer, implicit-explicit schemes, incompressible Navier-Stokes equations, large-eddy simulation, Lattice-Boltzmann method, natural convection, radiative heat transfer, relaxation scheme.