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

The boundary conditions prescribing the constant traction or the so-calleddo-nothing conditions are frequently taken on artificial boundaries in thenumerical simulations of steady flow of incompressible fluids, despite the factthat they do not facilitate a well-posed problem, not allowing to establish thestandard energy estimates. In a pursuit to understand better the possibleconsequences of using these conditions, we present a particular set of examplesof flow problems, where we find none or two analytical or numerical solutions.Namely, we consider problems where the flow connects two such artificialboundaries. In the simple case of the isotropic radial flows where both steadyand unsteady analytical solutions are derived easily, we demonstrate that whilefor some (large) boundary data all unsteady solutions blow up in finite time,for other data (including small or trivial) the unsteady flows either convergeasymptotically to one of two steady solutions, or blow up in finite time,depending on the initial state. We then document the very same behavior of thenumerical solutions for planar flow in a diverging channel. Finally, we providean illustrative example of two steady numerical solutions to the flow in athree-dimensional bifurcating tube, where the inflow velocity is prescribed atthe inlet, while the two outlets are treated by the do-nothing boundarycondition.

journal of mathematical fluid mechanics

On multiple solutions to the steady flow of incompressible fluids  subject to do-nothing or constant traction boundary conditions on artificial  boundaries