Integral Methods for Describing Pulsatile Flow

Abstract

Abstract. This paper presents an approximate solution of the pulsatile flow of a Newtonian fluid in the laminar flow regime in a rigid tube of constant diameter. The model is represented by two ordinary differential equations. The first equation describes the time evolution of the total flow rate, and the second equation characterizes the reverse flow near the wall. These equations are derived from the momentum balance equation and from the kinetic energy equation, respectively. The accuracy of the derived equations is compared with a solution in which the finite difference method is applied to a partial differential equation.

Computationally efficient finite element formulation for blood flow analysis in multi‐layered aorta modeled as viscoelastic material

“…One of the major drawbacks of the one-dimensional wave propagation models is that it requires a prior assumption of axial velocity profile across the cross-section in order to estimate the nonlinear and friction terms in the momentum equation. In the past, researchers have used flat velocity profile, [3][4][5][6] Poiseuille/parabolic velocity, 2,[7][8][9][10][11][12][13] and approximate velocity profile function of different degree polynomials 1,[14][15][16][17][18][19][20][21][22][23] in order to estimate the convection and diffusion terms. However, these widely considered axial velocity profile functions across the cross-section do not accurately capture the interaction between the blood and arterial wall, which is an essential feature of the blood flow through the arterial network.…”