A 2D nonlinear multiring model for blood flow in large elastic arteries

Abstract

In this paper, we propose a two-dimensional nonlinear “multiring” model to compute blood flow in axisymmetric elastic arteries. This model is designed to overcome the numerical difficulties of three-dimensional fluid–structure interaction simulations of blood flow without using the over-simplifications necessary to obtain one-dimensional blood flow models. This multiring model is derived by integrating over concentric rings of fluid the simplified long-wave Navier–Stokes equations coupled to an elastic model of the arterial wall. The resulting system of balance laws provides a unified framework in which both the motion of the fluid and the displacement of the wall are dealt with simultaneously. The mathematical structure of the multiring model allows us to use a finite volume method that guarantees the conservation of mass and the positivity of the numerical solution and can deal with nonlinear flows and large deformations of the arterial wall. We show that the finite volume numerical solution of the multiring model provides at a reasonable computational cost an asymptotically valid description of blood flow velocity profiles and other averaged quantities (wall shear stress, flow rate, ...) in large elastic and quasi-rigid arteries. In particular, we validate the multiring model against well-known solutions such as the Womersley or the Poiseuille solutions as well as against steady boundary layer solutions in quasi-rigid constricted and expanded tubes.