Higher order methods for fluid structure interaction problems

Multi-physics problems are ubiquitous in the real world and in engineering design. An important class of multi-physics problems are those of fluid-structure interactions (FSI) which involve an object governed by solid mechanics interacting with a fluid (e.g. a turbine interacting with the wind). Having reliable and efficient computer models for these problems are vital to understanding different natural physical systems and essential engineering problems. FSI problems are modeled mathematically by coupled partial differential equations (PDEs). Sophisticated numerical methods have been developed to approximate solutions of individual PDEs. However, the development of the state-of-the-art numerical methods for coupled PDEs remains a challenging task and continues to be a highly active and dynamic area of research. Training of at least one graduate student on the topics of the project is expected. As part of this effort, the development of provably stable higher-order splitting methods for FSI problems will be pursued. Splitting methods take advantage of fine-tuned numerical methods for fluid problems and solid problems. One solves each problem separately and they communicate via boundary conditions. The challenge is to make the methods both stable and higher-order accurate. Indeed, most of the numerical methods that are provably stable are low order accurate in time. The PI will build on the work done with collaborators using Robin-Robin methods. The Robin-Robin methods previously developed will be used as a base method for a more sophisticated correction method. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.