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, using the finite difference (1D) or the 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 the commercial software STAR-CCM+. The student should also acquire a good knowledge of the procedure needed to confirm the quality/accuracy of the numerical solution of a given thermal-fluid dynamic model.

As a minimum, the knowledge coming from traditional introductory courses in thermal fluid dynamics, e.g. from the course "Termofluidodinamica" in the Energy engineering BSc program at Politecnico di Torino, as well as in numerical analysis ("Calcolo numerico"), will be taken for granted. The former includes a basic knowledge of Navier-Stokes equations. The latter 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), together with some basic knowledge of MATLAB. As a reference for the students enrolled in the Energy and Nuclear engineering MSc program at Politecnico di Torino, the knowledge acquired in the course "Introduction to computational heat transfer" will be fully sufficient.

1D scalar advection problems
- The method of characteristics
- Finite difference methods
- The CFL condition
- MATLAB application

1D scalar advection-conduction problems
- Boundary layers
- Finite-difference methods
- Upwind vs. centered approximations
- MATLAB application

2D scalar advection-conduction problems
- The finite volume method
- MATLAB application

The incompressible Navier-Stokes laminar problem
- Scalar vs. vector problems: co-located vs. staggered grids, coupled vs. segregated solution, pressure correction methods (SIMPLE, ...).
- Classical benchmarks: lid-driven cavity; buoyancy driven cavity: derivation of a numerical correlation for the Nusselt number.
- STAR-CCM+ application

Introduction to the numerical solution of turbulent flow and heat transfer problems
- Reynolds Averaged Navier-Stokes (RANS)
- Classical benchmark: turbulent flow and heat transfer in a circular pipe
- STAR-CCM+ application and validation against experimental (e.g. Blasius, Dittus-Boelter) correlations.

30 hours of computational lab are foreseen, where the students will individually work on PCs, using the abovementioned software (MATLAB and STAR-CCM+). 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)
- R. Peyret, T.D. Taylor, Computational Methods for Fluid Flow (Springer, 1985)
- 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)
- D.C. Wilcox, Turbulence modeling for CFD , 3rd edition (DCW industries, 2006)
- H. K. Versteeg, W. Malalasekera, An Introduction to Computational Fluid Dynamics: The Finite Volume Method (Pearson Education, 2007)

Students are grouped in small teams.
Each team works on a model CFD problem, starting in the second part of the semester, where it is asked to:
1) solve the problem, using STAR-CCM+ and MATLAB, and summarize the results in the form of suitable plots;
2) justify the choice of the methods used to find the solution;
3) discuss the quality/accuracy of the computed solution.
These three items are collected by the team in a short report (pdf file), to be discussed with the Teaching Assistant, who will individually evaluate the authors of the report.
The students with a report evaluation > 24/30 go to the oral, which is focussed on the theory part of the course and on the discussion of one of the scripts developed by them in the MATLAB applications during the course.
For the rest of the students, the report evaluation gives the final mark.