Mathematical Sciences: Applied and Computational Mathematicsand Experimental Analysis

在这个项目中，首席研究员和他的同事将继续研究应用数学、数值分析和流体动力学的各个方面。特别是，他们将对自由边界的粘性流动、管道和通道内的粘性流动、各种水波问题以及波浪在倾斜海滩上的行为进行分析、数值和实验研究。他们将对数值技术进行理论分析，如多网格方法，这些方法在解决目前分析和实验能力之外的流体现象方面非常重要。流体动力学现象的研究对应用数学家提出了挑战，因为许多工作涉及数学分析、数值计算和实验室实验这三种基本技术之间的相互作用。考虑到这门学科的跨学科性质，为了成功地解决涉及流体流动的困难和重要问题，应用数学家必须与实验学家和计算科学家合作。在这个项目中，首席研究员组建了一个由流体动力学家组成的完美团队。数值分析和实验。他们的目标是继续他们在理解和量化粘性流动和水波的流体动力学方面的重要工作。

In this project the principal investigator and his colleagues will continue their research on various aspects of applied mathematics, numerical analysis and fluid dynamics. In particular, they will conduct analytical, numerical and experimental studies of viscous flows with free boundaries and viscous flows inside pipes and channels, a variety of water wave problems and the behavior of waves on sloping beaches. And they will perform theoretical analyses of numerical techniques like multi-grid methods that are so essential in resolving fluid phenomena that are beyond the present capabilities of analysis and experimentation. The study of fluid dynamical phenomena provides a challenge to applied mathematicians because so much of the work involves an interplay among the three basic techniques of mathematical analysis, numerical computation and laboratory experimentation. Given the interdisciplinary nature of the subject it is essential for applied mathematicians to collaborate with experimentalists and computational scientists, in order to tackle successfully difficult and important problems involving fluid flow. In this project the principal investigator has assembled the perfect team consisting of fluid dynamicists. numerical analysts and experimentalists. Their goal is to continue their important work on understanding and quantifying the fluid dynamics of viscous flows and water waves.