Semi-implicit and Implicit Solutions of Pulsatile Flow in the Axisymmetric Tube Using a Staggered Grid

We consider pulsatile flow of incompressible Newtonian fluid in a circular tube in the vicinity of an axisymmetric constriction. The problem is closely related e.g. to predictions of flow properties of blood in the vicinity of stenoses in blood vessels. Mathematically the problem is governed by the Navier-Stokes equation (here V is the velocity vector, p is the pressure, p the density, v is the coefficient of kinematic viscosity, t is time), and by the continuity equation div V = 0.