A new two-dimensional blood flow model with arbitrary cross sections

TL;DR

This paper introduces a novel two-dimensional blood flow model for arteries with arbitrary cross sections, derived from Navier-Stokes equations, and presents a positivity-preserving numerical scheme tested on idealized aorta simulations.

Contribution

It develops a new 2D blood flow model for arbitrary artery cross sections and proposes a well-balanced numerical scheme for accurate simulations.

Findings

The model accurately captures blood flow dynamics in complex artery geometries.

The numerical scheme preserves positivity and stability in simulations.

Simulations reveal effects of wall elasticity and perturbations on blood flow.

Abstract

A new two-dimensional model for blood flows in arteries with arbitrary cross sections is derived. The model consists of a system of balance laws for conservation of mass and balance of momentum in the axial and angular directions. The equations are derived by applying asymptotic analysis to the incompressible Navier-Stokes equations in narrow, large vessels and integrating in the radial direction in each cross section. The main properties of the system are discussed and a positivity-preserving well-balanced central-upwind scheme is presented. The merits of the scheme will be tested in a variety of scenarios. In particular, numerical results of simulations using an idealized aorta model are shown. We analyze the time evolution of the blood flow under different initial conditions such as perturbations to steady states consisting of a bulging in the vessel's wall. We consider different situations given by distinct variations in the vessel's elasticity.