Research on nonlinear waves of blood flow in arterial vessels

Abstract

In this paper, considering blood as an incompressible Newtonian fluid, we explore the propagation of blood flow. Based on the Navier–Stokes equations and the continuity equation, the vorticity equation is deduced. Then, using the multi-scale analysis and iterative perturbed method, we derive a new higher order nonlinear Schrödinger equation to describe the blood flow in the blood vessels. The traveling wave solution of the higher order equation is obtained with the help of the extended tanh-function method. By analyzing the higher-order term of the equation, we find that the width and velocity of the blood wave increase during the propagation process. To further study the numerical characteristic, the numerical solutions of the higher order nonlinear Schrödinger equation are obtained by the meshless radial basis function method. The absolute errors between the exact and numerical red solutions show that the meshless radial basis function method gives a more accurate solution. Finally, the influencing factors of stroke volume are discussed and analyzed which provide a strong theoretical basis for some blood diseases.