AIMS AND CONTENT

LEARNING OUTCOMES

The aim of the module is to provide the students with basic numerical techniques in order to solve parabolic, hyperbolic and elliptic partial differential equations, so that the students are able to solve problems relevant to their field of interest.

AIMS AND LEARNING OUTCOMES

Attendance and active participation in the proposed training activities (lectures, exercises and numerical exercises) and individual study will allow the student to:

• Derive a finite-difference approximation of arbitrary accuracy
• Identify if a non-uniform discretisation is necessary or not
• Predict the local and global truncation error for a given finite-difference approximation
• Formulate the discrete form of an ordinary or partial differential equation
• Plan a Design-of-Experiment (DoE) campaign for an experimental analysis
• Formulate a Response Surface Model (RSM) for a given set of DoE
• Solve numerically a linear ODE or PDE by integration in time 
• Evaluate the numerical stability characteristics of a certain discretisation

TEACHING METHODS

The lessons are divided into theory and practice. All the theory presented in the course is used in the exercises so that students can apply what they have learned and understand the difficulties in the applications. The exercises are both written and computer programming. Students are requested to bring their own computer and to install Matlab for which a student license is available. In the second part of the course an industrial software to perform computational fluid dynamics will be introduced and taught.

Working students and students with DSA, disability or other special educational needs certification are advised to contact the teacher at the beginning of the course to agree on teaching and exam methods which, in compliance with the teaching objectives, take into account individual ways of learning.

SYLLABUS/CONTENT

The program of the module includes the presentation and discussion of the following topics:​

• Introduction and motivation
• Introduction to matlab programming by video lectures and exercises in class
• NUMERICAL APPROXIMATIONS OF SYSTEM OF LINEAR EQUATIONS: Approximation with finite differences. Convergence, consistency, zero-stability and absolute stability. Forward Euler-centered scheme. Upwind, Lax-Friedrichs and Lax- Wendroff schemes. 
• INITIAL VALUE PROBLEMS: Analysis of the schemes, CFL condition and its meaning. Backward Euler-centered scheme. A quick description of systems and of non-linear problems.
• EXERCISES: basic derivations and analysis, solution of equations related to chemical engineering problems.
• HOME WORK: programming and derivations
• Design of Experiments (DoE)
• Response Surface Modeling (RSM) 
• Finite Volume Methods, Introduction to Ansys Fluent including tutorials 

RECOMMENDED READING/BIBLIOGRAPHY

• Quarteroni, Alfio; Saleri, Fausto; Gervasio, Paola , Scientific Computing with MATLAB and Octave, Editore: Springer, Anno edizione: 2010 
• Quarteroni, Alfio; Sacco, Riccardo; Saleri, Fausto , Numerical Mathematics, Editore: Springer, Anno edizione: 2007
• Optimization Methods: From Theory to Design by Marco Cavazzuti, Springer

TEACHERS AND EXAM BOARD

Exam Board

JAN OSCAR PRALITS (President)

ELISABETTA ARATO

CRISTINA ELIA MOLINER ESTOPIÑAN (President Substitute)

LESSONS

LESSONS START

https://corsi.unige.it/corsi/11428/studenti-orario

Class schedule

The timetable for this course is available here: Portale EasyAcademy

EXAMS

EXAM DESCRIPTION

The final exam consists in passing 1) two written tests or 2) an oral exam.

1)
There will be an intermediate test and a final test, the first during the lesson period and the second after the end of the course.

Each test consists of an exam with about 5 problems that must be solved with an analytical procedure. The duration of a test is 3 hours. Students will find examples of tests proposed in previous years in aulaweb and some of which, upon request by the students, are carried out in detail in class.

Students must pass each written test with a minimum grade of 18/30. The final grade is the average grade of the two tests. A failed test can be retaken during exam sessions. There will be 3 exam sessions for the 'winter' session (January, February and during the teaching break provided by the Politecnic School at Easter) and 3 exam sessions for the 'summer' session (June, July, September).

2)
For those who do not want to take the written tests, there is the possibility of an oral exam on the content of the whole course. The oral exam will take place during one of the scheduled sessions.

ASSESSMENT METHODS

Details on how to prepare for the exam and the degree of depth of each topic will be given during the lessons. The written tests will focus on 5 exercises and calculations on the topics indicated below.

The first test will be on the following topics: finite difference setting with arbitrary derivative and accuracy, numerical stability, convergence (local and global), discretization and grid (uniform and non), initial value problems

The second test will be on the following topics: Design of Experiment, Response Surface Modeling, the basis of Ansys Fluent

Exam schedule

FURTHER INFORMATION

Students with SLD, disability or other special educational needs certification are advised to contact the teacher at the beginning of the course to agree on teaching and exam methods that, in compliance with the teaching objectives, take into account the modalities learning opportunities and provide suitable compensatory tools.