A Comparison of Numerical Methods for the Hele-Shaw Equations

这是一项少数民族研究启动(MRI)计划赠款，旨在开发新的数值技术来研究两种流体之间的界面上的速度场。当一种流体在多孔介质中置换另一种流体时发生的微小扰动将受到特别关注。这些扰动导致界面稳定或不稳定。通常，这些界面是三维的，无论是实验还是数值研究都很困难。提议人将使用一种似乎可以处理这种性质的问题的代码。规划赠款将为一名训练有素的少数民族数学家提供支助，以编写一份竞争性提案，提交核磁共振研究启动部分。

This is a Minority Research Inititation (MRI) Planning Grant to develop new numerical techniques to study the velocity field in the interface between two fluids. Small disturbances that occur when one fluid displaces another fluid in a porous medium will receive special attention. These disturbances cause the interface to be stable or unstable. Usually, these interfaces are three-dimensional and difficult to study both experimentally and numerically. The proposer will use a code which appears to handle problems of this nature. The planning grant will provide support for a well-trained minority mathematician to prepare a competitive proposal to submit to the MRI research initiation component.