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 consider the fully-developed flow of an incompressible Newtonian fluid ina cylindrical vessel with elliptical cross-section (both an ellipse and theannulus between two confocal ellipses). In particular, we address an inverseproblem, namely to compute the velocity field associated with a given,time-periodic flow rate. This is motivated by the fact that flow rate is themain physical quantity which can be actually measured in many practicalsituations. We propose a novel numerical strategy, which is nonethelessgrounded on several analytical relations. The proposed method leads to thesolution of some simple ordinary differential systems. It holds promise to bemore amenable to implementation than previous approaches, which aresubstantially based on the challenging computation of Mathieu functions. Somenumerical results are reported, based on measured data for human blood flow inthe internal carotid artery, and cerebrospinal fluid (CSF) flow in the uppercervical region of the human spine. As expected, computational efficiency isthe main asset of our solution: a speed-up factor over 10^3 was obtained,compared to more elaborate numerical approaches. The main goal of the presentstudy is to provide an improved source of initial/boundary data for moreambitious numerical approaches, as well as a benchmark solution for pulsatileflows in elliptical sections with given flow rate. The proposed method can beeffectively applied to bio-fluid dynamics investigations (possibly addressingkey aspects of relevant diseases), to biomedical applications (includingtargeted drug delivery and energy harvesting for implantable devices), up tolonger-term medical microrobotics applications.

Pulsatile Viscous Flows in Elliptical Vessels and Annuli: Solution to the Inverse Problem, with Application to Blood and Cerebrospinal Fluid Flow