We present a fourth-order spatial accurate and practically stable compact difference scheme for the Cahn–Hilliard equation. The compact scheme is derived by combining a compact nine-point formula and linearly stabilized splitting scheme. The resulting system of discrete equations is solved by...

We consider an unconditionally gradient stable scheme for solving the Allen–Cahn equation representing a model for anti-phase domain coarsening in a binary mixture. The continuous problem has a decreasing total energy. We show the same property for the corresponding discrete problem by using...

We consider a second-order conservative nonlinear numerical scheme for the N-component Cahn–Hilliard system modeling the phase separation of a N-component mixture. The scheme is based on a Crank–Nicolson finite-difference method and is solved by an efficient and accurate nonlinear multigrid...

We present a practically unconditionally gradient stable conservative nonlinear numerical scheme for the N-component Cahn–Hilliard system modeling the phase separation of an N-component mixture. The scheme is based on a nonlinear splitting method and is solved by an efficient and accurate...

This paper presents a new diffuse interface model for multiphase incompressible immiscible fluid flows with surface tension and buoyancy effects. In the new model, we employ a new chemical potential that can eliminate spurious phases at binary interfaces, and consider a phase-dependent variable...