An efficient numerical method for the equations of steady and unsteady flows of homogeneous incompressible Newtonian fluid

In the present paper, we present some numerical methods to solve the equations of steady and unsteady flows, such as those in the microcirculatory bed and large blood vessels (arteries and veins), respectively. In the case of steady flows, the method does not need neither any boundary conditions on pressure nor any small parameter, and the main computation consists of solving some Poisson equations. In the case of unsteady flows, the scheme uses a consistent Neumann boundary condition for the pressure Poisson equation. At each time step, a Poisson and heat equation are solved for the pressure and each velocity component, respectively. The accuracy and efficiency of scheme are checked by a set of numerical tests.