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

In this paper, we present a general numerical platform for designingaccurate, efficient, and stable numerical algorithms for incompressiblehydrodynamic models that obeys the thermodynamical laws. The obtained numericalschemes are automatically linear in time. It decouples the hydrodynamicvariable and other state variables such that only small-size linear problemsneed to be solved at each time marching step. Furthermore, if the classicalvelocity projection method is utilized, the velocity field and pressure fieldcan be decoupled. In the end, only a few elliptic-type equations shall besolved in each time step. This strategy is made possible through a sequence ofmodel reformulations by fully exploring the models' thermodynamic structures.The generalized Onsager principle directly guides these reformulationprocedures. In the reformulated but equivalent models, the reversible andirreversible components can be identified, guiding the numerical platform todecouple the reversible and irreversible dynamics. This eventually leads todecoupled numerical algorithms, given that the coupling terms only involveirreversible dynamics. To further demonstrate the numerical platform's power,we apply it to several specific incompressible hydrodynamic models. The energystability of the proposed numerical schemes is shown in detail. Thesecond-order accuracy in time is verified numerically through time steprefinement tests. Several benchmark numerical examples are presented to furtherillustrate the proposed numerical framework's accuracy, stability, andefficiency.

A General Framework to Derive Linear, Decoupled and Energy-stable  Schemes for Reversible-Irreversible Thermodynamically Consistent Models: Part  I Incompressible Hydrodynamic Models