This project is concerned with the computational analysis of time dependent fluid flows and it involves both the design of reliable and efficient numerical methods for problems on unbounded domains and the simulation of wave propagation in reactive media. One aspect of this work is the development and testing of asymptotic boundary conditions for the Euler and Navier-Stokes equations in exterior and cylindrical domains. The main tool is the asymptotic analysis of the long range propagation of waves. An advantage of this approach is enhanced accuracy, which may be controlled by varying the domain size or improving the asymptotic approximations. A second area of concentration is the computational study of existence, stability and dynamics of multidimensional diffusive waves. One application is to a model of flame propagation in a channel, including the effects of heat loss at the walls. The numerical analysis of singular perturbation problems will also be studied. The emphasis is on hyperbolic problems with stiff source terms and on the long time simulation of complex systems. The unifying theme throughout is the interplay between computational and asymptotic analysis.
