an:06134437
Zbl 1259.65130
Lai, Huilin; Ma, Changfeng
Numerical study of the nonlinear combined sine-cosine-Gordon equation with the lattice Boltzmann method
EN
J. Sci. Comput. 53, No. 3, 569-585 (2012).
00312616
2012
j
65M06 76P05 82C40 35Q40 65M12
lattice Boltzmann method; sine-cosine-Gordon equation; Chapman-Enskog expansion; stability; finite difference method; evolution equation; numerical results
Summary: A lattice Boltzmann model is developed for solving the combined sine-cosine-Gordon equation through selecting equilibrium distribution functions properly. With the Chapman-Enskog expansion, the governing evolution equation is recovered correctly from the continuous Boltzmann equation. Some problems, which have exact solutions, are validated by the present model. From the simulations, we find that the numerical results agree well with the exact solutions or better than the numerical solutions reported in previous studies. The study indicates that the present method is very effective and accurate. The present model can be used to solve more other nonlinear wave problems.