Numerical study of the ternary Cahn–Hilliard fluids by using an efficient modified scalar auxiliary variable approach

Herein, we propose linear, decoupled, and energy dissipation-preserving schemes for the ternary Cahn–Hilliard (CH) fluid models by using a modified scalar auxiliary variable (MSAV) approach. The ternary CH model has extensive applications in material and fluid fields. When the classical scalar auxiliary variable (SAV) method is used for the ternary CH problem, extra computational costs are needed because of the decoupling between local and non-local variables. The MSAV method considered in this study not only inherits the merits of classical SAV method, i.e., linear scheme and energy stability, but also allows simpler calculations. In one time iteration, we only need to solve a set of linear equations by a step-by-step procedure, thus the computation is highly efficient. To accelerate the convergence, a fast linear multigrid algorithm is adopted to solve the resulting discrete systems. Various numerical tests without and with fluid flows are performed to verify the good performance of the proposed methods.