We construct a novel second-order time marching scheme with the full decoupling structure to solve highly coupled nonlinear two-phase fluid flow system consisting of nonlocal mass-conserved Allen–Cahn equation where two types regimes are considered (Navier–Stokes and Darcy). achieve decoupled by introducing variable designing an additional ordinary differential for it which plays key role maint...

In this paper we present an error analysis for a second order accurate numerical scheme the 2-D and 3-D Cahn–Hilliard (CH) equation, with improved convergence constant. The unique solvability, unconditional energy stability, uniform-in-time H2 stability of have already been established. However, standard estimate gives constant in exp(CT??m0), m0 positive integer interface width parameter ? bei...