An efficient scheme for a phase field model for the moving contact line problem with variable density and viscosity

Efficient energy stable numerical schemes for a phase field moving contact line model

“…The authors of Dong [6] and Dong and Shen [7] constructed some decoupled schemes for systems with variable density, however they did not provide any theoretical proof of discrete energy law for the decoupled schemes with dynamic contact line conditions. In Gao and Wang [14,15], Salgado [31] and Aland and Chen [1], the authors developed some energy stable schemes for the moving contact line problem with constant and/or variable densities. However, their schemes require solving a coupled nonlinear system for the phase function and velocity.…”

An energy stable C0 finite element scheme for a quasi-incompressible phase-field model of moving contact line with variable density

“…Our energy variational approach consistently yields both the correct bulk equations (the q-NSCH system) and a modified General Navier-Stokes Boundary Condition (GNBC) for the case of mass averaged velocity. The density effect on the contact line is explicitly modeled compared with the traditional GNBC [14,15,46,47,48,49] in the case of volume averaged velocity, where the effect is modeled implicitly by the bulk and boundary interactions.…”

Domain Decomposition Methods in Science and Engineering XXIII

“…We investigate locking effects in a hybrid version of a symmetric interior penalty (SIP) method, which is one of DG methods, and is called the HSIP method in this paper. Gao and Wang (2014) proposed a gradient stable semi-implicit finite difference scheme in 2D and 3D by using the convex splitting method for the Cahn-Hilliard equation and a projection method for the Navier-Stokes equations. The latter is called the numerical trace.…”