Incompressible Flows with Interfaces
|關鍵字:||不可壓縮流;流體界面;沈浸邊界法;曲面上之偏微分方程;界面/不規則區域藕合問題;非牛頓流體;水泡動態;三維乾型泡沫;Incompressible flow;Fluid interfaces;Immersed boundary method;PDEs on surfaces;Surface-bulk equations;Viscoelastic flow;Vesicle dynamics;3D dry foam simulation|
The study of the incompressible flows with interfaces is of major interests among applied mathematics community. It plays an important role in numerous natural phenomena and industrial applications, especially, for the hydrodynamics of micro-fluidic systems. For instance, the thin film flows in coating devices, the dynamics of liquid drops in ink-jet printing, the wetting phenomena on substrate, or even the hydrodynamics of water-walking insect, just to name a few. Since the complexity of effects associated with capillarity gains a more wide applications during the last century, the research effort spent on this topic is overwhelming in applied mathematics community. These effort brought in many remarkable successes in the understanding of the fundamental physics and the quantitative modeling of capillary phenomena in different problems. In this proposal, we shall focus our research topics on the different issues of mathematical modeling and numerical methods for incompressible flows with interfaces. In our previous NSC projects, NSC-97-2628-M-009-007-MY3 and NSC-98-2115-M-009-014-MY3, we have developed a series of numerical methods and applications for 2D interfacial flows. Therefore, in this proposal, we are moving forward to viscoelastic (non-Newtonian) flows and some 3D problems. In addition, we will also continue investigating the interfacial flows with soluble surfactant in which a coupled surface-bulk convection-diffusion equations must be solved. We will need to develop an efficient and also conservative scheme for those equations. In this proposal, we shall focus our research topics on the issues of mathematical modeling and numerical methods for the interfacial flows with interfaces. In particular, our research topics will concentrate on four different directions; namely, (1) 2D and 3D numerical schemes for solving coupled surface-bulk convection-diffusion equations with applications; (2) Numerical methods for viscoelastic interfacial flows; (3) Viscosity and inertia effects on vesicle dynamics and efficient algorithms for 3D vesicle problems; (4) 3D dry foam simulations and von Neumann law.