Lattice Boltzmann Model for Scroll Wave in Ginzburg-Landau Equation

The complex lattice Boltzmann model is proposed to simulate the scroll wave in three-dimensional Ginzburg-Landau equation. The method maintains the algorithmic simplicity of the original lattice Boltzmann scheme, and does not require an interpolation or coarse-graining procedure. We can see the details of the process of the scroll waves formed in three-dimensional space; we can see that the quantum vortex in three-dimension is still linear; we can see a variety of graceful movement patterns of the vortex filaments and their future destiny, which imply the results of the existing law on the vortex filaments predicted; we can also see that the accuracy of the simulation results can be compared with classical method. We inherited and developed our previous results on spiral waves in this book, and provided an alternative tool for simulating three-dimensional complex partial differential equation.