MI (1377) - INGEGNERIA AEROSPAZIALE / AEROSPACE ENGINEERING
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084796 - APPLIED COMPUTATIONAL FLUID DYNAMICS
Programma dettagliato e risultati di apprendimento attesi
Course objective The aim of the course is to enable graduate students to develop and employ modern algorithms for simulating both steady and unsteady incompressible flows giving a survey of state-of-the-art numerical methods. The course presents numerical methods for the numerical solution of the equations expressing the conservation laws of mass and momentum of an incompressible fluid. Spatial discretizations of local type (finite differences, volumes and elements) and of global type (spectral methods) will be considered to deal with problems of both engineering and fundamental interest.
Contents 1. Spatial discretization * Finite differences and the immersed-boundary method * Finite elements * Spectral and spectral-element methods * Stabilization for convection-dominated flows 2. Time discretization * Monolithic approach: time discretization (finite differences and Runge-Kutta schemes) * Time-splitting methods: exact-splitting methods, fractional-step methods.
References R.J. Leveque, Finite Difference Methods for Ordinary and Partial Differential Equations, SIAM, 2007. R. Temam, Navier-Stokes Equations Theory and Numerical Analysis, North-Holland Pub. Company, 1984 A. Ern & J.-L. Guermond, Theory and practice of finite elements, Springer, 2003. A. Quarteroni & A. Valli, Numerical approximation of partial differential equations, Springer, 2008 C.S. Peskin, The immersed boundary method, Acta Numerica, 11, 479–517, 2002. L. Quartapelle, Numerical solution of the Incompressible Navier–Stokes Equations, Birkauser, 1993. J.-L. Guermond, P. Minev & J. Shen, An overview of projection methods for incompressible flows, Comput. Methods Appl. Mech. Engrg., 195 (2006) 6011–6045 C. Canuto, M.Y. Hussaini, A. Quarteroni & T.A. Zang, Spectral methods in fluid dynamics, Springer, 1988. J. Shen, T. Tang & L. Wang, Spectral methods: algorithms, analysis and applications, Springer, 2011 P. Fischer, High-order methods for incompressible fluid flow, Cambridge University Press, 2002. G. Karniadakis & S. Sherwin, Spectral/hp Element Methods for CFD, Oxford University Press, 1999.
Note Sulla Modalità di valutazione
Each candidate will be assigned a project related to his/her own research and to the content of the lectures. During the exam, the candidate will present and discuss his/her project.
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