3 research outputs found
Numerical solution of phase field models for two-phase flows
Phase-field models describe the motion of multiphase flows using smooth interfaces across which the composition changes continuously. The phase-field variable represents a measure of phase as it quantifies relative differences or fractions of the fluid s components. The Cahn-Hilliard equation was originally proposed to model spinodal decomposition and coarsening in binary alloys. To this day, it has become broad ranged in its applicability. This thesis focuses on solving the Cahn-Hilliard equation numerically. A review of the mathematical modelling is made in order to develop numerical methods. Different numerical simulations in two dimensions are implemented to study the numerical and physical properties. Two realistic physical examples are also numerically solved
A multiphase Cahn-Hilliard system with mobilities and the numerical simulation of dewetting
We propose in this paper a new multiphase Cahn-Hilliard model with doubly
degenerate mobilities. We prove by a formal asymptotic analysis that it
approximates with second order accuracy the multiphase surface diffusion flow
with mobility coefficients and surface tensions. To illustrate that it lends
itself well to numerical approximation, we propose a simple and effective
numerical scheme together with a very compact Matlab implementation. We provide
the results of various numerical experiments to show the influence of mobility
and surface tension coefficients. Thanks to its second order accuracy and its
good suitability for numerical implementation, our model is very handy for
tackling notably difficult surface diffusion problems. In particular, we show
that it can be used very effectively to simulate numerically the dewetting of
thin liquid tubes on arbitrary solid supports without requiring nonlinear
boundary conditions.Comment: 35 page