Analytical and numerical investigation of hemodynamics of large vessels

Flow of blood in large vessels is described by non-stationary Euler equations for non-compressible fluid.
In the general case the geometry of blood vessels is such that the flow is three-dimensional. However, there exists a large number or large blood vessels in which we can assume the flow to be onedimensional. In this case the system of equations contains just independent variables $x$ and $t$, and two functions to be determined (pressure and velocity), thus being hyperbolic system of partial equations that allows for existence of two families of real characteristics.
For analytical and numerical investigation of this system the same approaches are used as for onedimensional non-stationary problems of gas dynamics, using Riemann invariants.
Examples of the actual computations and test problems for some large arteries are given. Distributions of parameters in vessels are presented, including cases when the artery is squeezed. A qualitative interpretation of Korotkov tones is presented.