  We show that a single particle distribution for the D2Q13 lattice Boltzmann
scheme can simulate coupled effects involving advection and diffusion of
velocity and temperature. We consider various test cases: non-linear waves with
periodic boundary conditions, a test case with buoyancy, propagation of
transverse waves, Couette and Poiseuille flows. We test various boundary
conditions and propose to mix bounce-back and anti-bounce-back numerical
boundary conditions to take into account velocity and temperature Dirichlet
conditions. We present also first results for the de Vahl Davis heated cavity.
Our results are compared with the coupled D2Q9-D2Q5 lattice Boltzmann approach
for the Boussinesq system and with an elementary finite differences solver for
the compressible Navier-Stokes equations.
