A spectral-element discontinuous Galerkin lattice Boltzmann method for simulating natural convection heat transfer in a horizontal concentric annulus

We present a spectral-element discontinuous Galerkin lattice Boltzmann method to solve incompressible natural convection flows based on the Bousinessq approximation. A passive-scalar thermal lattice Boltzmann model is used to resolve flows for variable Prandtl number. In our model, we solve the lattice Boltzmann equation for the velocity field and the advection-diffusion equation for the temperature field. As a result, we reduce the degrees of freedom when compared with the passive-scalar double-distribution model, which requires the solution of several equations to resolve the temperature field. Our numerical solution is represented by the tensor product basis of the one-dimensional Legendre-Lagrange interpolation polynomials. A high-order discretization is employed on body-conforming hexahedral elements with Gauss-Lobatto-Legendre quadrature nodes. Within the discontinuous Galerkin framework, we weakly impose boundary and element-interface conditions through the numerical flux. A fourth-order Runge-Kutta scheme is used for time integration with no additional cost for mass matrix inversion due to fully diagonal mass matrices. We study natural convection fluid flows in a square cavity and a horizontal concentric annulus for Rayleigh numbers in the range of Ra = 10(3)-10(8). We validate our numerical approach by comparing it with finite-difference, finite-volume, multiple-relaxation-time lattice Boltzmann, and spectral-element methods. Our computational results show good agreement in temperature profiles and Nusselt numbers using relatively coarse resolutions. (c) 2014 Elsevier Ltd. All rights reserved.