Numerical methods for two-phase incompressible flows with mass transport

在这个项目中，我们开发，分析和实施数值方法模拟两相不可压缩流与质量传输。溶解的物质的质量传输是由一个依赖于时间的对流扩散方程结合适当的耦合条件在接口建模。该方程的解在两相之间的未知界面上一般是不连续的，在我们的应用中，这个问题通常是对流主导的。这造成了严重的数字困难。我们计划开发新的稳定和有效的有限元离散方法，这个输运方程。严格的误差分析和这些方法的应用将进行调查。这些方法将在我们小组提供的软件包（DROPS）中实现。DROPS软件包的流体动力学和质量传输的数值模拟将与一个合作伙伴合作进行验证，该合作伙伴来自一个关于微型通道中泰勒流的实验项目。

In this project we develop, analyze and implement numerical methods for the simulation of two-phase incompressible flows with mass transport. The mass transport of a dissolved species is modeled by a time-dependent convection-diffusion equation combined with appropriate coupling conditions at the interface. The solution of this equation is in general discontinuous across the unkown interface between the two phases and in our applications this problem is often convection-dominated. This causes severe numerical difficulties. We plan to develop new stable and efficient finite element discretization methods for this transport equation. Both a rigorous error analysis and the application of these methods will be investigated. The methods will be implemented in a software package (DROPS) that is available in our group. The numerical simulation of fluid dynamics and mass transport with the DROPS package will be validated in collaboration with a partner from an experimental project on Taylor flows in mini-channels.