Abstract: Convection Cahn-Hilliard (abbreviated as C-H) system is a class of continuum medium models,which can be used to explore phase transitions in binary systems. Applications of C-H system have been so ubiquitous in solid theory,excitable mathematics,material science and so on, therefore, great attentions have been paid by researchers in recent years from the characteristics of high nonlinearity,rich and complicated dynamical phenomena. In this paper,it is proposed that improved Lattice Boltzmann (LB for short) method with source term from the spatial derivatives of high order to simulate 1D-convetion C-H system. According to such LB model,transfer matrix of system and the stable condition of numerical computation are explored,which are closely related to the ratio of lattice spacing and time step. Based on such LB model,interesting research results are realized:on one hand,the growing convection strength k decreases oscillation range of system A,and power law feature of k-A relationship is found independent of diverse initial states. On the other hand,although the growth of convection strength can promote oscillation frequency of system,frequency hopping phenomena are outstanding. Furthermore,different initial states can lead to periodic oscillations with different frequencies,which mean that oscillations with different frequencies can coexist in the same convection strength.

Key words: Lattice Boltzmann method, convection Cahn-Hilliard equation, oscillation range, power law, frequency hopping, frequency coexistence, chaos