Comparison of Simulations of Convective Flows (Communications in Computational Physics, 2018)
We show that a single particle distribution for the "energy-conserving" D2Q13 lattice Boltzmann scheme can simulate coupled effects involving advectionand diffusion of velocity and temperature. We consider various test cases: non-linearwaves with periodic boundary conditions, a test case with buoyancy, propagation oftransverse waves, Couette and Poiseuille flows. We test various boundary conditionsand propose to mix bounce-back and anti-bounce-back numerical boundary conditionsto take into account velocity and temperature Dirichlet conditions. We presentalso first results for the de Vahl Davis heated cavity. Our results are compared withthe coupled D2Q9-D2Q5 lattice Boltzmann approach for the Boussinesq system andwith an elementary finite differences solver for the compressible Navier-Stokes equations.Our main experimental result is the loss of symmetry in the de Vahl Davis cavitycomputed with the single D2Q13 lattice Boltzmann model without the Boussinesqhypothesis. This result is confirmed by a direct Navier Stokes simulation with finitedifferences.