Comparison of Simulations of Convective Flows
This work offers a simplified lattice Boltzmann method for thermal flows, but the improvements are incremental as similar results are achieved with existing approaches.
The authors demonstrate that a single D2Q13 lattice Boltzmann distribution can simulate advection-diffusion of velocity and temperature, achieving comparable results to coupled D2Q9-D2Q5 and finite difference solvers across multiple test cases including the de Vahl Davis cavity.
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.