A lattice-Boltzmann relaxation scheme for coupled convection–radiation systems

The convection–radiation effects in thermal fluid flows are studied based on the lattice-Boltzmann method. Nine-velocity flow and temperature distributions are used to obtain the mass, momentum and energy equations in thermal incompressible flows by studying equivalent moment systems. The radiative heat flux in the energy equation is obtained using the discrete-ordinates solution of the radiative transfer equation. A non-oscillatory relaxation scheme is used to solve the coupled moment equations. Such schemes have the advantage of being simple and easy to implement. Numerical results are presented for two test examples on coupled convection–radiation flows in two dimensional enclosures. Detailed simulation results at different flow and radiative regimes, as well as benchmark solutions, are presented and discussed.