English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Having a finite interfacial thickness, the phase-field models supply a way tomodel the fluid interfaces, which allows the calculations of the interfacemovements and deformations on the fixed grids. Such modeling is applied to thecomputation of two-phase incompressible Stokes flows in this paper, leading toa system of Stokes-Cahn-Hilliard equations. The Stokes equation is modified byadding the continuum force $ - c \nabla w $, where $ c $ is the order parameterand $ w $ is the chemical potential of $ c $. Similarly, the advection effectsare modeled by addition of the term $ \vec{u} \cdot \nabla c $ in theCahn-Hilliard equation. We hereby discuss how the solutions to the aboveequations approach the original sharp interface Stokes equation as theinterfacial thickness $ \varepsilon$ tends to zero. We start with a microscopicmodel and then the homogenized or upscaled version to the same from author'sprevious work, cf. \cite{lakhmara2022}, where the analysis and homogenizationof the system have been performed in detail. Further, we perform the numericalcomputations to compare the outcome of the effective model with the originalheterogeneous microscale model.

Numerical Validation for a Stokes-Cahn-Hilliard System in a Porous Medium