A novel fully-decoupled, second-order and energy stable numerical scheme of the conserved Allen–Cahn type flow-coupled binary surfactant model

In this paper, we establish a binary fluid surfactant model by coupling two mass-conserved Allen–Cahn equations and the Navier–Stokes consider numerical simulations of developed model. Due to large number nonlinear nonlocal terms in model, it is very challenging design an efficient accurate scheme, especially full decoupling scheme with second-order time accuracy. We solve challenge developing novel fully-decoupled approach, where key idea achieving structure introduce ordinary differential equation deal that satisfy so-called “zero-energy-contribution” property. way, can easily discretize coupled fully explicit while still maintaining unconditional energy stability. By combining projection type method quadratization at each step, only need several linear elliptic constant coefficients. strictly prove solvability satisfies stability, give various 2D 3D show its stability accuracy numerically. As far as author knows, first time-accurate flow-coupled phase-field