Newtonian Flow in Converging-Diverging Capillaries

The one-dimensional Navier-Stokes equations are used to derive analytical expressions for the relation between pressure and volumetric flow rate in capillaries of five different converging-diverging axisymmetric geometries for Newtonian fluids. The results are compared to previously-derived expressions for the same geometries using the lubrication approximation. The results of the one-dimensional Navier-Stokes are identical to those obtained from the lubrication approximation within a non-dimensional numerical factor. The derived flow expressions have also been validated by comparison to numerical solutions obtained from discretization with numerical integration. Moreover, they have been certified by testing the convergence of solutions as the converging-diverging geometries approach the limiting straight geometry.Comment: 23 pages, 5 figures, 1 table. This is an extended and improved version. arXiv admin note: substantial text overlap with arXiv:1006.151

Comparing Poiseuille with 1D Navier-Stokes Flow in Rigid and Distensible Tubes and Networks

A comparison is made between the Hagen-Poiseuille flow in rigid tubes and networks on one side and the time-independent one-dimensional Navier-Stokes flow in elastic tubes and networks on the other. Analytical relations, a Poiseuille network flow model and two finite element Navier-Stokes one-dimensional flow models have been developed and used in this investigation. The comparison highlights the differences between Poiseuille and one-dimensional Navier-Stokes flow models which may have been unjustifiably treated as equivalent in some studies.Comment: 26 pages, 6 figure

Dynamic Transmission Conditions for Linear Hyperbolic Systems on Networks

We study evolution equations on networks that can be modeled by means of hyperbolic systems. We extend our previous findings in \cite{KraMugNic20} by discussing well-posedness under rather general transmission conditions that might be either of stationary or dynamic type - or a combination of both. Our results rely upon semigroup theory and elementary linear algebra. We also discuss qualitative properties of solutions