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 Tools annual

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 Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

We study the process of two-phase flow in thin porous media domains ofBrinkman-type. This is generally described by a model of coupled, mixed-typedifferential equations of fluids' saturation and pressure. To reduce the modelcomplexity, different approaches that utilize the thin geometry of the domainhave been suggested.  We focus on a reduced model that is formulated as a single nonlocal evolutionequation of saturation. It is derived by applying standard asymptotic analysisto the dimensionless coupled model, however, a rigid mathematical derivation isstill lacking. In this paper, we prove that the reduced model is the analyticallimit of the coupled two-phase flow model as the geometrical parameter ofdomain's width--length ratio tends to zero. Precisely, we prove the convergenceof weak solutions for the coupled model to a weak solution for the reducedmodel as the geometrical parameter approaches zero.

On the limit of a two-phase flow problem in thin porous media domains of Brinkman-type