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.