Numerical simulation of complex flows involving elastic membranes, fluid-fluid and fluid-solid interfaces

多组分和多相流的数值模拟在化学和生物医学工程中有着重要的应用。在过去，我们已经开发了算法和计算机代码来直接模拟粘性流体中刚性颗粒、液滴和气泡的动力学。在接下来的五年里，我们计划扩展自由边界算法，将考虑弹性膜存在的表面流变学纳入其中，这样我们就可以模拟血细胞在剪切流动中的行为。在许多实际情况下，红细胞会受到巨大的剪切，比如人工心脏瓣膜周围的血流，它们通常无法承受施加在它们身上的压力。因此，数值模拟它们在各种剪切流中的行为和估计它们的生存机会是很重要的。到目前为止，该算法的另一个应用是模拟具有复杂形状的运动物体的流动。一个很好的例子是渐进式空腔泵。我们正计划对这种流动进行广泛的数值模拟。最后，我们将继续研究与我们开发的算法相关的数值分析中的一些基本问题。

The numerical simulation of multicomponent and multiphase flows has important applications in Chemical and Biomedical Engineering. In the past we have developed algorithms and computer codes for the direct simulation of the dynamics of rigid particles and drops and bubbles in viscous fluids. During the next five years we plan to extend the free boundary algorithms to incorporate a surface rheology that accounts for the presence of elastic membranes so that we can simulate the behaviour of blood cells in shear flows.  The red blood cells are subjected to large shears in many practical situations like the flow around artificial heart valves for example, and often they can not survive the stress exerted on them.  Therefore, it is important to simulate numerically their behaviour in a variety of shear flows and estimate their chances to survive.Another application of the algorithms developed so far is for the simulation of flows involving moving objects with a complex shape.  A good example are the progressive cavity pumps.  We are planning to do extensive numerical simulations of such flows.Finally we will continue the work on some fundamental issues in Numerical Analysis related to the algorithms that we develop.