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 Open

Presents the pdf analysis as premium feature

PDF Analysis

Insights

Presents the summarisation as premium feature

Summarisation

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

The purpose of this work is to construct a simple, efficient and accuratewell-balanced numerical scheme for one-dimensional (1D) blood flow in largearteries with varying geometrical and mechanical properties. As the steadystates at rest are not relevant for blood flow, we construct two well-balancedhydrostatic reconstruction techniques designed to preserve low-Shapiro numbersteady states that may occur in large network simulations. The Shapiro number Sh = u/c is the equivalent of the Froude number for shallow water equations andthe Mach number for compressible Euler equations. The first is the low-Shapirohydrostatic reconstruction (HR-LS), which is a simple and efficient method,inspired from the hydrostatic reconstruction technique (HR). The second is thesubsonic hydrostatic reconstruction (HR-S), adapted here to blood flow anddesigned to exactly preserve all subcritical steady states. We systematicallycompare HR, HR-LS and HR-S in a series of single artery and arterial networknumerical tests designed to evaluate their well-balanced and wave-capturingproperties. The results indicate that HR is not adapted to compute blood flowin large arteries as it is unable to capture wave reflections and transmissionswhen large variations of the arteries' geometrical and mechanical propertiesare considered. On the contrary, HR-S is exactly well-balanced and is the mostaccurate hydrostatic reconstruction technique. However, HR-LS is able tocompute low-Shapiro number steady states as well as wave reflections andtransmissions with satisfying accuracy and is simpler and computationally lessexpensive than HR-S. We therefore recommend using HR-LS for 1D blood flowsimulations in large arterial network simulations.

Low-Shapiro hydrostatic reconstruction technique for blood flow simulation in large arteries with varying geometrical and mechanical properties