The course focuses on what is commonly called Computational Fluid Dynamics (CFD). The core of the course is devoted to the development and application of methods for the numerical solution of 1D and 2D/3D thermal-fluid dynamics problems, within the framework of the finite difference (1D) and finite volume (2D/3D) approaches. Some emphasis is also put on the fundamental concepts of benchmark, verification and validation.

Through this course the student is expected to acquire a good knowledge of the above-mentioned methods, as well as the ability to perform simple CFD simulations using commercial and/or open-source software such as: Ansys-Fluent, STAR CCM+, OpenFoam, .... The student should also acquire a good knowledge of the procedure needed to confirm the quality/accuracy of the numerical solution of a given thermalfluid dynamic model.

As a minimum, the knowledge coming from a traditional introductory course in numerical analysis ("Calcolo numerico") will be taken for granted. This includes: basic numerical linear algebra (direct and iterative methods for the solution of large algebraic sets of equations), elementary methods for the numerical solution of nonlinear algebraic problems, numerical quadrature formulae, numerical integration of ordinary differential equations (initial value problems); ability to use Matlab. As a reference for the students enrolled in the Energy and Nuclear engineering program at Politecnico di Torino, the knowledge acquired in the MSc course "Introduction to computational methods for energy applications" will be fully sufficient.

1D scalar advection problems (6h)
- The method of characteristics
- Finite difference methods
- The CFL condition
- Matlab application

1D scalar advection-conduction problems (6h)
- Boundary layers
- Finite-difference methods
- Upwind vs. centered approximations
- Matlab application

2D scalar advection-conduction problems (6h)
- The finite volume method
- Approximation of the fluxes
- Imposing boundary conditions
- Matlab application

The incompressible Navier-Stokes laminar problem (6h)
- Scalar vs. vector problems: co-located vs. staggered grids, coupled vs. segregated solution, pressurecorrection methods (SIMPLE, ...).
- Approximation of the fluxes
- Classical benchmarks: lid-driven cavity; buoyancydriven cavity: derivation of a numerical correlation for the Nusselt number.
- Ansys-Fluent vs. StarCCM+ vs. OpenFoam application

Introduction to the numerical solution of turbulent flow and heat transfer problems (6h)
- Direct Numerical Simulation (DNS) vs. Large Eddy Simulation (LES) vs. Reynolds Averaged Navier-Stokes (RANS)
- Classical benchmark: turbulent flow and heat transfer in a circular pipe
- Ansys-Fluent vs. StarCCM+ vs. OpenFoam application and validation against experimental correlations.

30 hours of computational lab are foreseen, where the students will individually work on PCs, using the different abovementioned software. Special emphasis will also be put on the issue of mesh generation.

Selected chapters from:
- J. M. Cooper, "Introduction to Partial Differential Equations with MATLAB" (Birkhaeuser, 2000)
- C. Hirsch, "Numerical Computation of Internal and External Flows", 2nd ed. (Butterworth-Heinemann, 2007)
- J. H. Ferziger, M. Peric, "Computational Methods for Fluid Dynamics", 3rd ed. (Springer, 2013)
User manuals of the different software.

The assessment is made by written exam only. Each student works on a PC in the lab and is asked to: 1) solve a model CFD problem, using one of the above-mentioned software, and summarizing the results in the form of suitable plots; 2) justify the choice of the methods used for the solution; 3) discuss the quality/accuracy of the obtained numerical solution. These three items, collected by the student in a short report (doc file), contribute as follows to the final grade: 1) 60%; 2) 20%; 3) 20%.