Although blood flows in a pulsatile fashion, little consideration has been given in past studies to its instantaneous resistance to motion when onset and cessation of flow occur abruptly. Hemorheological studies have documented three kinds of blood flow properties. 1) Shear thinning is a fall in viscolity as shear rate rises. 2) Viscoelasticity is a transient shear stress variation due to elastic deformation of erythrocytes. Dilatancy is a viscoelasticity-modifying property attributed to high shear rate erythrocyte rigidity; viscoelasticity is prominent only at low shear rate. 3) Thixotropy is an initial extra flow resistance linked to developing orientation and disaggregation of erythrocytes. Thixotropy returns fully to blood over a period longer than 1 min. Measurements utilizing a fast response Couette viscometer have revealed an extra 10% transient flow resistance after a flow cessation shorter than that between heart beats. The rapidly recovered transient flow resistance has a temporal pattern similar to thixotropy. Its peak and duration are directly related to total shear strain (shear rate x time) over the 8-30 s-1 shear rate range studied. Transient behavior was essentially identical in analyses carried out using three different viscometer gaps. Numerical simulation to test the effect of the newly observed transient behavior on sudden onset tube flow shows that the developing pattern of pulsatile arterial flow can be affected by its presence.
To study the flow behavior in regions where hemodynamic effects have been suggested to participate in atherogenesis, we evaluated flow in a mold of the aorta and renal arteries of a previously healthy 27-year-old woman who died of trauma. A birefringent solution (vanadium-pentoxide) was used. When diluted, this material behaves like a Newtonian fluid. This method gives a complete picture of the entire flow field. Zones of flow separation and disturbed flow can be seen and the location and size of disturbed areas observed. Unseparated flow regions downstream from disturbed zones can be properly visualized and the method can be used for pulsatile flow as well as steady flow. During steady flow (only at branch to-trunk flow ratios greater than 0.20), zones of flow separation were observed in the aorta distal to the renal arteries. During pulsatile flow, disturbances were found at nearly all branch-to-trunk flow ratios.
SUMMARYStandard preconditioners such as incomplete LU decomposition perform well when used with conjugate gradient-like iterative solvers such as GMRES for the solution of elliptic problems. However, efficient computation of convection-dominated problems requires, in general, the use of preconditioners tuned to the particular class of fluid-flow problems at hand. This paper presents three such preconditioners. The first is applied to the finite element computation of inviscid (Euler equations) transonic and supersonic flows with shocks and uses incomplete LU decomposition applied to a matrix with extra artificial dissipation. The second preconditioner is applied to the finite difference computation of unsteady incompressible viscous flow; it uses incomplete LU decomposition applied to a matrix to which a pseudo-compressible term has been added. The third method and application are similar to the second, only the LU decomposition is replaced by Beam-warming approximate factorization. In all cases, the results are in very good agreement with other published results and the new algorithms are found to be competitive with others; it is anticipated that the efficiency and robustness of conjugate-gradient-like methods will render them the method of choice as the difficulty of the problems that they are applied to is increased.
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