Aeronautical engineering

Relevant mathematical models in aerodynamics. Different kinds of governing partial differential equations. Initial and boundary conditions. Numerical solution of PDE: domain discretization, accuracy, stability, consistency and convergence. Fundamentals of the finite difference solution of the governing equations. Finita difference solution of the 1D heat equation: explicit and implicit schemes. 2D Fourier equation and transport (advection-diffusion) equation. ADI and approximate factorization schemes. Solution of ODE with boundary layer behaviour. Numerical schemes for elliptic equations. Numerical solution of the Navier-Stokes equations in primitive variables and in vorticity-streamfunction.

Basic knowledge of the governing equation in fluid dynamics as well as of the related physics.

C.A.J. Fletcher "Computational Techniques for Fluid Dynamics", Springer Verlag, Berlin, 1988. P. J. Roache "Fundamentals of Computational Fluid Dynamics", Hermosa Publ., Albuquerque, 1998. Further material provided by the teacher

classroom lessons

The exam is composed by a written test followed by an oral discussion. During the written trial, the student is required to discuss two of the problem analyzed during the course. Further comments and details are requested in the oral discussion.