Lattice Boltzmann Method For A Class Of Nonlinear Partial Differential Equations And Their Numerical Simulation

Lattice Boltzmann Method(LBM)is a new numerical simulation method between macro and micro scales,and it has a lot of advantages,such as clear physical background,simple programming,easy border processing,suitable for large-scale parallel computing,etc.In this paper,for a class of nonlinear wave equations and composite KdV-Burgers equations,several high precision schemes were developed.Using Chapman Enskog multi-scale technique and Taylor expansion methods,the equilibrium distribution functions in the model are derived and verified by some numerical examples.Firstly,several basic models and corresponding processing methods about LBM are introduced;Secondly,a lattice BGK model(D1Q4)of the one-dimensional nonlinear wave equation presented,using Chapman Enskog multi-scale technique and Taylor expansion methods,the corresponding macro equation is restored,and the equilibrium distribution functions in the model and boundary conditions are obtained;Then,a lattice BGK model(D1Q5)of the composite KdV-burgers equations is conducted by using a correction function;Finally,some numerical examples are presented to verify the validity of the model,and at the same time,the error analysis is given for these models.