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/

Zendy Plus

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

Zendy Tools

Zendy Open

We present an adaptive simulation framework for binary-fluid flows, based onthe Abels-Garcke-Gr\"un Navier-Stokes-Cahn-Hilliard (AGG NSCH)diffuse-interface model. The adaptive-refinement procedure is guided by atwo-level hierarchical a-posteriori error estimate, and it effectively resolvesthe spatial multiscale behavior of the diffuse-interface model. To improve therobustness of the solution procedure and avoid severe time-step restrictionsfor small-interface thicknesses, we introduce an $\varepsilon$-continuationprocedure, in which the diffuse interface thickness ($\varepsilon$) areenlarged on coarse meshes, and the mobility is scaled accordingly. To furtheraccelerate the computations and improve robustness, we apply a modifiedBackward Euler scheme in the initial stages of the adaptive-refinementprocedure in each time step, and a Crank--Nicolson scheme in the final stagesof the refinement procedure. To enhance the robustness of the nonlinearsolution procedure, we introduce a partitioned solution procedure for thelinear tangent problems in Newton's method, based on a decomposition of theNSCH system into its NS and CH subsystems. We conduct a systematicinvestigation of the conditioning of the monolithic NSCH tangent matrix and ofits NS and CH subsystems for a representative 2D model problem. To illustratethe properties of the presented adaptive simulation framework, we presentnumerical results for a 2D oscillating water droplet suspended in air, and wevalidate the obtained results versus those of a corresponding sharp-interfacemodel.

A Robust and Accurate Adaptive Approximation Method for a Diffuse-Interface Model of Binary-Fluid Flows