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

While various phase-field models have recently appeared for two-phase fluidswith different densities, only some are known to be thermodynamicallyconsistent, and practical stable schemes for their numerical simulation arelacking. In this paper, we derive a new form of thermodynamically-consistentquasi-incompressible diffuse-interface Navier-Stokes Cahn-Hilliard model for atwo-phase flow of incompressible fluids with different densities. Thederivation is based on mixture theory by invoking the second law ofthermodynamics and Coleman-Noll procedure. We also demonstrate that our modeland some of the existing models are equivalent and we provide a unificationbetween them. In addition, we develop a linear and energy-stabletime-integration scheme for the derived model. Such a linearly-implicit schemeis nontrivial, because it has to suitably deal with all nonlinear terms, inparticular those involving the density. Our proposed scheme is the first linearmethod for quasi-incompressible two-phase flows with nonsolenoidal velocitythat satisfies discrete energy dissipation independent of the time-step size,provided that the mixture density remains positive. The scheme also preservesmass. Numerical experiments verify the suitability of the scheme for two-phaseflow applications with high density ratios using large time steps byconsidering the coalescence and break-up dynamics of droplets includingpinching due to gravity.

Diffuse-Interface Two-Phase Flow Models with Different Densities: A New Quasi-Incompressible Form and a Linear Energy-Stable Method