PERIODO:

Computational thermal Fluid Dynamics (CtFD) constitues a key ingredient in the design and analysis of complex engineering systems of industrial interest and in applied research in general.
The course has introductory character: the fundamentals of the three classes of computational methods most used today (finite differences, finite elements and finite volumes) are presented and discussed.
The problems addressed start from the study of simple scalar, steady state, one-dimensional models (e.g., for advection-diffusion), to reach at the end of the course vector, transient, multi-dimensional models (e.g., for lid- and buoyancy-driven cavities).
We adopt an engineering appoach, finalized on the one hand to the critical understanding of the fundamentals of the different computational methods, on the other hand to the quality assurance of the numerical solution.
PREREQUISITES: some knowledge of numerical methods and heat transfer, at the level provided by dedicated undergraduate courses.

Navier-Stokes equations in integral and differential form. [2 hrs]
Analysis and solution of an advection-diffusion, scalar model problem in 1D and 2D [12 hrs]
Finite differences o Upwind schemes o Time marching o Consistency, stability, convergence o Non-linear problems o Alternating Direction Implicit (ADI) method.
Ref.: R. Peyret, T.D. Taylor, Computational Methods for Fluid Flow (Springer, 1985)
Finite elements o Weak formulation o Galerkin and Petrov-Galerkin (SUPG) methods o Mesh generation, adaptive methods o Computation of the elemental matrix and assembly of the global matrix o Error estimates o Comparison with finite differences
Ref.: C. Johnson, Numerical solutions of PDEs by the finite element method (Cambridge UP, 1987)
Finite volume methods for the solution of 2D incompressible Navier-Stokes problems [6 hrs] o Conservation laws o Approximation of the fluxes and numerical quadrature formulae o Internal and external iterations, staggered vs. non-staggered grids o Pressure correction (SIMPLE, SIMPLEC, PISO methods).
Ref.: J. H. Ferziger, M. Peric, Computational Methods for Fluid Dynamics (Springer, 2001)