An efficient dimension splitting p-adaptive method for the binary fluid surfactant phase field model

In this paper, an efficient p-adaptive numerical algorithm is proposed for solving two-and three-dimensional (2D and 3D) binary fluid surfactant phase field models. The equation is a coupled system of a fourth-order nonlinear Cahn-Hilliard equation and a second-order nonlinear diffusion equation. There are three new ideas about algorithm design. Firstly, the high-dimensional equation is split into an array of one-dimensional sub-problems that could be solved via parallel processes. Secondly, global stability is constructed by guaranteeing the local stability of the sub-problems, and the one-dimensional problems are solved by a stabilized semi -implicit scheme with the fourth-order compact difference discretization. Finally, with the extrapolation method for convergence order improvement, a temporal p-adaptive strategy, which dynamically selects the order of extrapolation according to the speed of energy change, is developed to ensure efficiency and high precision. Besides that, the proposed numerical algorithm gratifies the discrete mass conservation properties and can be easily programmed. Via numerical testing, it has good convergence performance and computational stability. Numerical simulations including the surfactant absorption and coarsening dynamics verify the effectiveness of the algorithm.