Lattice Boltzmann model for complex Ginzburg–Landau equation in curvilinear coordinates

A lattice Boltzmann model is proposed for solving the complex Ginzburg–Landau equation (CGLE) with curvilinear coordinates. The method maintains the algorithmic simplicity of the original lattice Boltzmann scheme, and does not require an interpolation or coarse-graining procedure. This lattice Boltzmann scheme is based on uniformly distributed lattice points in these curvilinear coordinate systems. The algorithm provides advantages similar to the previous lattice Boltzmann method in that it is easily adapted to CGLE. The numerical simulations show spiral wave on a disc, the surface of a sphere, and the inside of a sphere. Examples show that the model accurately reproduces the phenomena in the CGLE.