The principal investigator will study various problems associated with the numerical solution of differential equations that govern incompressible and compressible flows of fluids. In particular, he will study vortex methods for incompressible flows, the numerical capturing of oscillatory solutions of gasdynamic equations, and the use of dispersive approximations in the solution of compressible flow problems. Fluid flow problems in two and three space dimensions are governed by complicated systems of nonlinear partial differential equations. Often the only practical way to solve such systems is to use a computer to generate approximate numerical solutions. But this is not all that easy either. The principal investigator will use what is called a vortex method to generate numerical solutions of the equations of incompressible and compressible fluid flow. This basic method and the improvements on it made by the principal investigator allow one to find accurate solutions in an efficient manner.
