On a novel fully-decoupled, linear and second-order accurate numerical scheme for the Cahn–Hilliard–Darcy system of two-phase Hele–Shaw flow

We construct a novel fully-decoupled and second-order accurate time marching numerical scheme with unconditional energy stability for the Cahn–Hilliard–Darcy phase-field model of two-phase Hele–Shaw flow, in which, key idea to realize full decoupling structure is use so-called “zero-energy-contribution” function design special ordinary differential equation deal nonlinear coupling terms between flow field variable. Compared existing type schemes, developed here more effective, efficient easy implement. At each step, one only needs solve few linear equations constant coefficients. also strictly prove solvability scheme, implement various simulations 2D 3D show efficiency proposed numerically.