Abstract
In this paper, we consider numerical approximations of the binary surfactant phase-field model on complex surfaces. Consisting of two nonlinearly coupled Cahn–Hilliard type equations, the system is solved by a fully discrete numerical scheme with the properties of linearity, decoupling, unconditional energy stability, and second-order time accuracy. The IGA approach based on Loop subdivision is used for the spatial discretizations, where the basis functions consist of the quartic box-splines corresponding to the hierarchic subdivided surface control meshes. The time discretization is based on the so-called explicit-IEQ method, which enables one to solve a few decoupled elliptic constant-coefficient equations at each time step. We then provide a detailed proof of unconditional energy stability along with implementation details, and successfully demonstrate the advantages of this hybrid strategy by implementing various numerical experiments on complex surfaces.
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