本研究運用數值方法來計算脈衝流(pulsatile flow)於彈性頸縮管(elastic tube)內之流場變化。血液被視為不可壓縮之Newtonian 流體，流場之統御方程式則為不可壓縮形式之非定常(unsteady)Navier-Stokes 方程組。在薄管壁之假設下，運用彈性力學中應力及應變之力平衡導出管壁運動之方程式。管內流體與管壁運動之交互作用(fluid-structure interaction)乃透過流體施加於管壁上的力與管壁位移速度作動態之耦合(dynamical coupling) ， 並採用雙時步(dual time-step) 虛擬壓縮性法(pseudo-compressibility)配合有限體積法(finite-volume formulation)來求得Navier-Stokes 方程式之數值解。 In this study, we apply a numerical scheme to calculate a pulsatile flow in an elastic tube with variable cross section. The purpose is to simulate the blood flow in arterial vessels and to study its dynamics. The blood is assumed to be an incompressible Newtonian fluid, and the flow field is governed by a set of unsteady incompressible Navier-Stokes equations. Under the assumption of a thin-wall tube, the motion of the tube wall can be derived from a force-balance equation using an elastic stress-strain relation. Dynamic coupling of the fluid flow and the tube-wall motion through the pressure at the tube wall is considered in this formulation. In the fluid part, the time-dependent incompressible Navier-Stokes equations are first written into a conservative hyperbolic form and then solved by using a dual time step plus pseudo-compressibility strategy. A finite volume formulation is adopted, and an upwind difference combined with the TVD scheme is applied to evaluate the flux terms.
