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.
