High order methods for incompressible fluid flow: Application to moving boundary problems.

The focus of this project is simulation tools for studying problems with free surfaces or moving boundaries. The objectives are to develop verifyably accurate and fast computational methods, and to apply such simulation tools to a couple of selected probl ems. The first is a simulation-based study of large-scale Benard-Marangoni convection. One of the intriguing features with this problem is the formation of hexagonal convection cells from random initial conditions. We plan to study the details of the very small free surface deformation, as well as the sensitivity of geometric irregularities on the pattern selection. For example, it has been observed experimentally that a small dent in the bottom surface may change the hexagonal cells in the vicinity of th e dent to diamond-shaped cells. Such simulations have never been done before. The second problem we plan to study is a model problem inspired by the use of elastic fabric containers for transportation of fresh water. Unlike the Benard-Marangoni convection , the free surface deformation can now be large, and computational tools are needed for accurate tracking of moving fronts. We expect to the able to develop new and verifyably improved tools for handling the time evolution of surfaces and volumes. The res ults from this project could be of interest to microfluidics and to marine technology.