Search

Blood flow in distensible arteries is nonlinear and time-dependent. The radial motion of the wall alters the dimension and geometry of the flow field. The nonlinear pulsating flow processes are successfully computed by mapping the wavy flow field to a fixed domain and by casting the geometric, kinematic and dynamic parameters of the flow into a dimensionless form of the Navier–Stokes equations. The complexity of the equations is compensated by a significant advantage in finite difference solutions. It is accomplished by using a fixed regular mesh network to model time-dependent irregular meshes in the physical domain for boundary layer development and vortices in pulsatile flows.

Nonlinear pulsatile blood flows in distensible vessels were calculated using an implicit finite-difference scheme. The time-dependent wavy lumen was mapped to a fixed rectangular domain. The transient geometric, kinematic, and dynamic boundary conditions were grouped as dimensionless parameters in the Navier-Stokes equations. The flow was controlled by a time-dependent von Karman number and the dilatation and contraction of the wall. Local acceleration components along the wall, the inlet, and the outlet were employed in the determination of the Neumann boundary condition for the pressure field. The momentum flux associated with wall motion had a significant effect on the flow rate and the resistance coefficient. The interaction of the main flow and flow separation was dominated by flow acceleration and deceleration.

Axisymmetric laminar blood flows in a stenotic model vessel are calculated by using a finite-difference scheme of the Navier-Stokes equations. The wavy lumen are transformed to a rectangular region with fine and irregular meshes mapped to regular ones in the computational domain. The pulsating flow is controlled by a time-dependent von Karman number. At the upstream and downstream ends, the local acceleration is employed to replace the Neumann boundary condition for solving the pressure field from the divergence of the Navier-Stokes equations, resulting in a new treatment on the inlet and outlet conditions for transient flow problems. The kinematic and dynamic characteristics of vortices in the pulsating flow processes are analyzed along with the pressure and shear fields.