The public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing the burden, to the Department of Defense, Executive Service Directorate (0704'()188). Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to any penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number. The objective of this research is to conduct DNS studies of hypersonic boundary layer receptivity, transient growth and transition with surface roughness. The main approach is to use DNS as a research tool to study the boundary layer receptivity and transient-growth mechanisms in hypersonic flows, including the development of numerical algorithms and parallel computer codes of higher order numerical methods for the simulation of hypersonic flows with surface roughness of fmite heights. During the three-year period, we have conducted DNS studies on the hypersonic boundary layer flows over flat plates and blunt cones. A new high-order cut -cell method has been developed for the numerical simulation of hypersonic boundary layer transition with finite height surface roughness. The method has been applied to the numerical simulations of two-dimensional hypersonic flows over a flat plate. Furthermore, the stabilization effect of the surface porous coating over a flat plate is extensively studied by series of numerical simulations. We also collaborate with Prof. Tumin in the University of Arizona to compare numerical and theoretical results on receptivity of a Mach 5.92 flow over a flat plate to wall blowing-suction, and to analyze the nonparallel flow effect.