Facoltà di Ingegneria - Guida degli insegnamenti (Syllabus)

The knowledge of the fundamentals of fluid-dynamics is highly recommended.

The course aims at giving students the advanced knowledge about the computational fluid dynamics subject. Another aim is to integrate the fundamentals of fluid dynamics, gas dynamics and aerodynamics. The course provide advanced knowledge on fluid dynamics simulation techniques. This knowledge completes the previous engineering education enhancing the expertise in the field of mechanical engineering. Students deepen the main thermofluid dynamics phenomena becoming aware of the multidisciplinary context of engineering with particular focus on the issues related to the approach to new design problems

In order to apply the acquired knowledge, students should be able to face complex design problems and to manage innovation and development of new products and new technological processes. In particular, they must be able to choose and apply the suitable analytical and modelling tools to simulate at best the behavior of plants/components of both heat transfer and propulsion systems. The final goal is to be able to predict and improve the performance of the system/components under investigation. The main skills acquired in the course are: 1. Knowledge about the numerical discretization of the fluid dynamics governing equations; 2. Knowledge about the turbulence modelling; 3. Ability to use a fluid dynamics simulation tool and the capability to critically analyse of the obtained results

The ability of solving numerical problems, together with the awareness of their knowledge, will improve the judgement autonomy of students, their communications skills and their learning ability

Elements on the classification of partial differential equations; Recalls about the NavierStokes equations and about the constitutive equation for Newtonian flows. Integral and differential forms of the equations. Conservative form. Incompressible and compressible governing equations. Boundary conditions for the Navier-Stokes equations. Discretization of a model equation, the finite differences, the finite volumes and finite elements approaches. Consistency, convergence and stability of a numerical scheme. Rate of convergence, dissipation and dispersion errors. Time integration with explicit and implicit schemes. The finite volumes approach in multi-dimensional cases, application of the method to the Euler governing equations. Approximation of volume and surface integrals. Numerical fluxes, the Riemann problem and the exact and approximated solvers. The diffusive terms for Navier-Stokes equations. The peculiarity of the incompressible case, derivation of the discrete Poisson equation for pressure. Grid generation process for fluid dynamics applications. The turbulence modelling: the Reynolds averaged Navier-Stokes equations and the closure models. Differential models with one or more differential equations. Large Eddy Simulation (LES) and Direct Numerical Simulation (DNS) of turbulent flows. Theoretical lessons will be supported by practical exercises in a computer lab. To fully understanding the proprieties of a numerical discretization scheme simple programs for solving model equations will be used. Commercial and/or open source software will be employed for solving real fluid dynamics problems (aerodynamics, termo-fluid dynamics etc )

The method for learning evaluation will consist in an oral interview. During this examination the candidate will be interviewed on the main proprieties of a numerical discretization scheme and about the turbulence modeling introduced during the course. It will be also considered the students ability in using those concepts for a proper set up of a computational fluid dynamics model.

t will be evaluated the students ability to autonomously formulate and set up a computational fluid dynamics simulation for a problem proposed within the examination. The ability to motivate with technical considerations the choices performed in approaching the computational fluid dynamics problem will be considered as well as the capability to critically analyse and interpret the results of the simulation. Morover, the student must demonstrate his/her knowledge of the main proprieties of a discretization scheme (for partial differential equations) as well as about the turbulence modelling. The maximum mark is awarded to students that demonstrate in the test a complete autonomy in formulating and solving the problems, with an outstanding ability to use the methodologies, the mathematical and physical models proper of the computational fluid dynamics field. The minimum mark is awarded to students that demonstrate the ability to solve the test with sufficient knowledge of the methodologies, the mathematical and physical models proper of the computational fluid dynamics field.

IGrading scheme is based on a scale of 30 points. Successful completion of the examination will lead to grades ranging from 18 to 30.

The final grade will be the sum of the grades obtained in answering three questions. The maximum grade obtained for each question will be 10 points. The laude grade will be assigned to students who obtained 30 points as well as proved a complete understanding of all the subjects of the course.

All the slides used during the course can be downloaded from the moodle web page: https://lms.univpm.it. Basic reference textbook: C. Hirsch , Numerical Computation of Internal and External Flows: The Fundamentals of Computational Fluid Dynamics, 2nd Edition, ISBN:9780750665940 For further investigation: H. Versteeg, W. Malalasekera, An Introduction to Computational Fluid Dynamics: The Finite Volume Method, 2nd Edition, Pearson, ISBN-13: 9780582218840 Anderson, J.D.Jr, "Computational Fluid Dynamics The Basics with Applications", McGraw-Hill, 1995. ISBN 0-07-001685-2. Ferziger, J.H. and M. Peric, "Computational Methods for Fluid Dynamic", Springer, 2002. ISBN 3-540-42074-6.

- Ingegneria Meccanica (Corso di Laurea Magistrale (DM 270/04))

**Università Politecnica delle Marche**

P.zza Roma 22, 60121 Ancona

Tel (+39) 071.220.1, Fax (+39) 071.220.2324

P.I. 00382520427