The research to be performed will be in the following areas: Computational and Analytical Problems in Neutron Transport Theory (C. Borgers). Problems from rarefied gas dynamics and neutron transport will be studied. 1) Gas film lubrication is traditionally modeled by the Reynolds equation, derived from the compressible Navier-Stokes equations. Here an approach based on the simplest kinetic model, free molecular flow, is proposed. 2) Discrete analogs of this statement will be studied, with emphasis on time discretization. Viscous Systems of Hyperbolic Conservation Laws and Hamilton-Jacobi Equations (E. Harabetian). This proposal concerns the analysis and development of numerical techniques for problems in hyperbolic conservation laws and their viscous perturbation, and Hamilton-Jacobi equations. The specific problems proposed are 1) Multidimensional front propagation for hyperbolic conservation laws and the modeling of viscous effects. 2) Convergence to a steady state for Hamilton-Jacobi equations, with application to "shape for shading" problems. Vortex Sheet Computations (R. Krasny). Various aspects of vortex sheet motion will be studied. 1) The vortex blob method will be extended and applied to splitter plate flow. 2) Compact cutoff functions and multipole algorithms for vortex sheet motion will be investigated. 3) Vortex blob, Navier Stokes, and experimental results for wake flow will be compared, to asses he effect of neglecting physical viscosity in the vortex sheet model. 4) Axisymmetric vortex sheet roll-up will be computed, in free space and at the edge of a round pipe.
