2024/10/14 by Jinpeng Zhang, Li Luo, Zhang, Jinpeng +3
Engineering · Materials Science · #FOS: Mathematics #Fluid Dynamics and Thin Films #Numerical Analysis (math.NA) #Solidification and crystal growth phenomena
paper · pdf · doi:10.48550/arxiv.2410.10195
openalex publication_date 2024/10/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we develop a second-order, fully decoupled, and energy-stable numerical scheme for the Cahn-Hilliard-Navier-Stokes model for two phase flow with variable density and viscosity. We propose a new decoupling Constant Scalar Auxiliary Variable (D-CSAV) method which is easy to generalize to schemes with high order accuracy in time. The method is designed using the "zero-energy-contribution" property while maintaining conservative time discretization for the "non-zero-energy-contribution" terms. Our algorithm simplifies to solving three independent linear elliptic systems per time step, two of them with constant coefficients. The update of all scalar auxiliary variables is explicit and decoupled from solving the phase field variable and velocity field. We rigorously prove unconditional energy stability of the scheme and perform extensive benchmark simulations to demonstrate accuracy and efficiency of the method.