A novel linear, unconditional energy stable scheme for the incompressible Cahn–Hilliard–Navier–Stokes phase-field model

2020 ◽  
Vol 80 (12) ◽  
pp. 2948-2971
Author(s):  
Hongen Jia ◽  
Xue Wang ◽  
Kaitai Li
Keyword(s):  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Navier Stokes ◽  
Energy Stable ◽  
Energy Stable Scheme ◽  
Stable Scheme

Phase Field Modeling of Nonequilibrium Patterns on the Surface of a Liquid Film Under Lateral Oscillations at the Substrate

2014 ◽  
Vol 24 (09) ◽  
pp. 1450110 ◽  
Author(s):  
Rodica Borcia ◽  
Michael Bestehorn
Keyword(s):  
Liquid Film ◽  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Solid Substrate ◽  
Navier Stokes ◽  
Bottom Plate ◽  
Navier Stokes Equation ◽  
Harmonic Vibrations ◽  
Spatial Dimensions

We use a phase field model which couples the generalized Navier–Stokes equation (including the Korteweg stress tensor) with the continuity equation for studying nonlinear pattern formation on the surface of a liquid film under (linear and circular) lateral harmonic vibrations at the solid substrate. First, we prove the thermodynamic consistency of our phase field model. Next, we present computer simulations in three spatial dimensions. We illustrate nonequilibrium patterns at the instability onset, confirming in this way the results recently reported in Phys. Rev. E 88, 023025 (2013). The lateral profiles of the deflected surface are compared with those reported in J. Fluid Mech. 686, 409 (2011) for Faraday instability excited by vertical harmonic vibrations at the bottom plate.

Sign in / Sign up

Export Citation Format

Share Document