Spatiotemporal lattice Boltzmann model for the three-dimensional cubic-quintic complex Ginzburg-Landau equation

A spatiotemporal lattice Boltzmann model for solving the three-dimensional cubic-quintic complex Ginzburg-Landau equation (CQCGLE) is proposed. Different from the classic lattice Boltzmann models, this lattice Boltzmann model is based on uniformly distributed lattice points in a three-dimensional spatiotemporal space, and the evolution of the model is about a spatial axis rather than time. The algorithm possesses advantages similar to the lattice Boltzmann method in that it is easily adapted to complex Ginzburg-Landau equations. Examples show that the model reproduces the phenomena in the CQCGLE accurately.