Comparison of Simulations of Convective Flows

TL;DR

This paper demonstrates that a single particle distribution in the D2Q13 lattice Boltzmann scheme can effectively simulate coupled advection and diffusion effects in convective flows, tested across various flow scenarios.

Contribution

It introduces a unified lattice Boltzmann approach for simulating coupled convective effects, including novel boundary condition mixing and initial results for heated cavity flows.

Findings

Successful simulation of non-linear waves and buoyancy effects

Effective boundary condition implementation for velocity and temperature

Comparison shows competitive accuracy with finite difference methods

Abstract

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.