| Abstract: |
| In this work we consider the coupling between the incompressible Navier-Stokes equations with the viscous Cahn-Hilliard equations, coupling that models the motion of isothermal mixture of two confined immiscible and incompressible fluids with comparable densities and viscosities. The dynamic boundary conditions that we endow the model with, take into account the existence of a moving contact line defined at the intersection of the fluid-fluid interface with the solid wall of the physical domain. For this model we propose an energy stable temporal scheme and we prove the unconditional solvability and the stability of the discretization proposed. We also propose a fully discrete scheme for which we prove the stability and we present some numerical simulations for this problem. |
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