Two complementary lattice-Boltzmann-based analyses for nonlinear systems

Lattice Boltzmann models that asymptotically reproduce solutions of nonlinear systems are derived by the Chapman-Enskog method and the analytic method based on recursive substitution and Taylor-series expansion. While both approaches yield identical hydrodynamic equations and can be generalized to analyze a variety of nonlinear systems, they have complementary advantages and disadvantages. In particular, the error analysis is substantially easier using the Taylor-series expansion method. In this work, the Burgers', Korteweg-de Vries, and Kuramoto-Sivashinsky equations are analyzed using both approaches, and the results are discussed and compared with analytic solutions and previous studies.