Through this course the student is expected to acquire a good knowledge of the above-mentioned methods, as well as the ability to perform CtFD simulations using the commercial software STAR-CCM+. The student should also acquire a good knowledge of the procedures needed to confirm the quality/accuracy of the numerical solution of a given thermal-fluid dynamic model. At the end of the course you should be ready to make good use of CtFD in your professional life -- a likely event.

The knowledge coming from traditional introductory courses in thermal fluid dynamics, e.g. from the course “Termofluidodinamica” in the Energy engineering BSc program, 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, the knowledge acquired in the course "Introduction to computational heat transfer" (Energy and Nuclear engineering MSc program) or “Laboratorio Computazionale di Scambio Termico” (Energy engineering BSc program), will be sufficient.

1D transient scalar advection problems - The method of characteristics; - Finite difference methods; - The CFL condition. 1D steady-state scalar advection-conduction problems - Boundary layers; - Finite-difference methods; - Upwind vs. centered approximations. 2D scalar advection-conduction problems - The finite volume method. 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. Introduction to the numerical solution of turbulent flow and heat transfer problems - Reynolds Averaged Navier-Stokes (RANS); - Classical benchmark: backward-facing step; turbulent flow and heat transfer in a circular pipe.

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30 hours of lectures are foreseen on the above-mentioned topics. 30 hours of computational laboratory are foreseen on the above-mentioned topics, where the students will individually work on PCs, using MATLAB and STAR-CCM+.

Notes/slides provided by the lecturers. 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)

Exam: Compulsory oral exam; Group project;

The exam consists of a compulsory group project on the computational laboratory and (for a subset of the students, see below) of an oral part on the material presented during the lectures. Group project: Students are grouped in teams (pairs). Each team works on a CtFD Project, starting in the second part of the semester, where it is asked to: – solve the problem, using STAR-CCM+, and summarize the results in the form of suitable plots; – justify the choice of the methods used to find the solution; – discuss the quality/accuracy of the computed solution. These three items are collected by the team in a short report (PDF file). The Teaching Assistants will discuss with the team and then evaluate the individual contribution of the authors. The teams have two options: • Produce one MATLAB script (chosen by the team between two alternatives) + the Project report  computational laboratory mark up to 30L, OR • Produce the Project report only  computational laboratory mark up to 27. For the students with a computational laboratory mark ≤ 24/30, this is the final mark. The students with a computational laboratory mark > 24/30 will go to the oral  final mark = max (70% computational laboratory mark + 30% oral mark, 24).

Exam: Compulsory oral exam; Group project;

.The exam consists of a compulsory group project on the computational laboratory and (for a subset of the students, see below) of an oral part on the material presented during the lectures. Group project: Students are grouped in teams (pairs). Each team works on a CtFD Project, starting in the second part of the semester, where it is asked to: – solve the problem, using STAR-CCM+, and summarize the results in the form of suitable plots; – justify the choice of the methods used to find the solution; – discuss the quality/accuracy of the computed solution. These three items are collected by the team in a short report (PDF file). The Teaching Assistants will discuss with the team and then evaluate the individual contribution of the authors. The teams have two options: • Produce one MATLAB script (chosen by the team between two alternatives) + the Project report  computational laboratory mark up to 30L, OR • Produce the Project report only  computational laboratory mark up to 27. For the students with a computational laboratory mark ≤ 24/30, this is the final mark. The students with a computational laboratory mark > 24/30 will go to the oral  final mark = max (70% computational laboratory mark + 30% oral mark, 24).