| Abstract: |
| In this talk we briefly show the derivation of a thermodynamically consistent phase field model. Then we will show how to design a mass conservative, energy stable, finite difference method on a staggered grid for the system of the two-phase flow equations with variable density and viscosity. We also present an efficient, practical nonlinear multigrid method - comprised of a standard FAS method for the Cahn-Hilliard equation, and a method based on the Vanka-type smoothing strategy for the Navier-Stokes equation - for solving these equations. We test the scheme in the context of Capillary Waves, rising droplets and Rayleigh-Taylor instability. Quantitative comparisons are made with existing analytical solutions or previous numerical results that validate the accuracy of our numerical schemes. This is a joint work with ZL Guo et al. |
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