Finite difference, finite volume, finite element, and spectral methods, consistency, stability and convergence of numerical schemes, governing equations for reacting flows, convection, diffusion, convection-diffusion problems, matrix solution methods-cyclic reduction, Fourier, Jacobin, Gauss Siedel, Sor, Adi, Chebschev acceleration, Lax-Wendroff scheme, Mccormack scheme, transonic small disturbance equation solution, staggered grids, simple scheme, discrete Fourier transform. Students work on two substantial projects using commercial software. Restricted to College of Engineering and Applied Science Graduate Students or BS/MS Mechanical Engineering Concurrent Degree students. Prerequisites: Restricted to College of Engineering and Applied Science Graduate Students or BS/MS Mechanical Engineering or Concurrent Degree students.