The Cahn-Hilliard equation (CHE) is widely used in modeling two-phase fluid flows, and it is critical to solve this equation accurately to track the interface between the two phases. In this paper, a high-order lattice Boltzmann equation model is developed for the CHE via the fourth-order Chapman-Enskog expansion. A truncation error analysis is performed, and the leading error term proportional to the Peclet number is identified. The results are further confirmed by the Maxwell iteration. With the inclusion of a correction term for eliminating the main error term, the proposed model is able to recover the CHE up to third order. The proposed model is tested by several benchmark problems. The results show that the present model is capable of tracking the interface with improved accuracy and stability in comparison with the second-order one.

• Received 26 September 2018
• Revised 26 March 2019

DOI:https://doi.org/10.1103/PhysRevE.99.043310