Lattice Boltzmann method for the convection-diffusion equation in curvilinear coordinate systems

A lattice Boltzmann method for simulating convection and diffusion using a curvilinear grid system is presented. The proposed method does not require an interpolation or coarse-graining procedure, and thus maintains the algorithmic simplicity of the original lattice Boltzmann scheme. The lattice Boltzmann scheme is based on uniformly distributed lattice points in a transformed coordinate system, and the apparent anisotropy of diffusion that arises due to the coordinate transformation is properly handled using the multiple-relaxation-time collision operator. An asymptotic analysis of the lattice Boltzmann equation shows that the proposed method appropriately reproduces the transformed convection-diffusion equation. Several specific problems are numerically analyzed in order to validate the proposed method, including an axially symmetric (two-dimensional) problem in which the diffusion flux at an oblate hemispheroid is simulated using a body-fitted orthogonal curvilinear grid system.