The Presidential Young Investigator will conduct research in the area of computational fluid dynamics; in particular, he will study shock diffractions and bifurcations as different shocks interact with each other and with fluid interfaces and vortex sheets. This is very important and timely research, and it is of sufficient complexity that the PI will employ analytical methods from geometry and bifurcation theory, in addition to computational techniques. The goals of the research are twofold. The first goal is to discover different types of wave patterns that result from the complex interactions of shocks and fluid structures, while the second goal is to develop numerical methods that allow one to follow the evolution in time of the waves generated by the interactions. Many phenomena in fluid dynamics arise out of the interactions of different types of waves with each other and with internal fluid structures such as interfaces. What makes these interactions difficult to study mathematically is that they are described by systems of nonlinear differential equations, and so one must use computers in order to generate solutions. But this is tricky also, because computers can often generate meaningless information, unless the numerical methods used are reliable. The PI will study such problems with "intelligent" numerical methods. These are methods that have sufficient analytical and physical theory built into them that they produce sharp approximations to the correct physical solutions.
