A novel decoupled second-order time marching scheme for the two-phase incompressible Navier–Stokes/Darcy coupled nonlocal Allen–Cahn model

A second order in time, decoupled, unconditionally stable numerical scheme for the Cahn-Hilliard-Darcy system

We propose a novel second order in time, decoupled and unconditionally stable numerical scheme for solving the Cahn-Hilliard-Darcy (CHD) system which models two-phase flow in porous medium or in a Hele-Shaw cell. The scheme is based on the ideas of second order convex-splitting for the Cahn-Hilliard equation and pressure-correction for the Darcy equation. We show that the scheme is uniquely sol...

Decoupled Energy Stable Schemes for a Phase-Field Model of Two-Phase Incompressible Flows with Variable Density

We consider in this paper numerical approximations of two-phase incompressible flows with different densities and viscosities. We present a variational derivation for a thermodynamically consistent phase-field model that admits an energy law. Two decoupled time discretization schemes for the coupled nonlinear phase-field model are constructed and shown to be energy stable. Numerical experiments...

Decoupled Energy Stable Schemes for a Phase Field Model of Three-Phase Incompressible Viscous Fluid Flow

We develop a numerical approximation for a hydrodynamic phase field model of three immiscible, incompressible viscous fluid phases. The model is derived from a generalized Onsager principle following an energetic variational formulation and is consisted of the momentum transport equation and coupled phase transport equations. It conserves the volume of each phase and warrants the total energy d...

Second-order scheme for quadrature-based velocity high order moment methods for disperse two-phase flows

Decoupled, Energy Stable Schemes for Phase-Field Models of Two-Phase Incompressible Flows

We construct in this paper two classes, based on stabilization and convex splitting, of decoupled, unconditionally energy stable schemes for Cahn-Hilliard phase-field models of two-phase incompressible flows. At each time step, these schemes require solving only a sequence of elliptic equations, including a pressure Poisson equation. Furthermore, all these elliptic equations are linear for the ...