Professors Osher, Engquist, and others will continue their individual and joint research on the development analysis and applications of numerical methods for nonlinear partial differential equations. Specific methods to be studied include: essentially nonoscillatory shock capturing techniques, front capturing algorithms, multiresolution and wavelet based methods, numerical homogenization, effective boundary conditions, kinetic models, spectral and viscosity methods, particle methods, and stochastic difference methods. Engineering and physical applications to be studied include: aerodynamical properties of high speed vehicles, hydrodynamic device models, miscible flow in porous media, combustion, reacting gas flows, shock turbulence interactions, microwave scattering, Boltzmann equations, nuclear fusion reactors, and core-annular flows. This broad range of activity has value both in its own right and with regard to extensive applications.
