A lattice kinetic scheme for incompressible viscous flows with heat transfer

A lattice kinetic scheme for incompressible viscous flows with heat transfer is developed based on the lattice Boltzmann method. In the new scheme, macroscopic variables are calculated without velocity distribution functions. Thus, the scheme can save computer memory because there is no need to store the velocity distribution functions. Governing equations for the macroscopic variables are obtained by applying the asymptotic theory. The continuity equation, the Navier-Stokes equations. and the convection-diffusion equation for fluid temperature are obtained with relative errors of O(epsilon(2)) where epsilon is a small parameter that is of the same order as a lattice spacing and is related to a relaxation parameter. In order to veri v the accuracy of the scheme, natural convection flows in a square cavity are simulated, and the calculated results are in good agreement with available standard results.