Second-Order, Energy-Stable and Maximum Bound Principle Preserving Schemes for Two-Phase Incompressible Flow

Abstract In this paper, we propose several linear fully discrete schemes for the mass-conserved Allen-Cahn-Navier–Stokes equation, based on the generalized stabilized exponential scalar auxiliary variable approach in time and the marker and cell (MAC) scheme in space. It is quite remarkable that our schemes can guarantee second-order accuracy in space provided the maximum bound principle (MBP) is satisfied, whereas most previous work can only possess first-order accuracy in space. We rigorously show that the constructed schemes satisfy the unconditional energy dissipation law and preserve the MBP. Finally, various numerical examples are presented to verify the theoretical results and demonstrate the efficiency of the proposed schemes.