34606 - Numerical Methods for Energetics (Graduate Course)

Learning outcomes

At the end of the course, the student has knowledge of the techniques for numerical resolution and the computational tools of major importance in the field of energy engineering. The student will also be able to implement such numerical resolution techniques in MATLAB environment.

Course contents

Module 1

• Numerical problems and algorithms; direct and iterative algorithms
• Machine numbers, computer memory, fundamental operations
  Vector and matrix norms
• Errors in numerical analysis (rounding, idealization, truncation, discretization, conditioning); error propagation in numerical analysis: robust algorithms, unavoidable error
• Iterative processes: convergence criterion, convergence speed; error propagation in an iterative process: problem conditioning, amplification factor, well and poorly conditioned problems
• Ordinary or partial differential equations, not dependent on time: discretization by finite difference method; solution of the resulting numerical problems by diagonalization, direct methods (Thomas and ADI algorithms) and iterative methods (Jacobi, Gauss-Seidel and SOR); power method
• Linear and nonlinear, time-dependent differential equations: discretization by finite difference method; temporal integration (Euler and trapezoid methods); solution of numerical problems resulting from the application of explicit and implicit numerical schemes
• Integral equations, not dependent on time: discretization using quadrature formulas; solution of the numerical problem by Gauss method with partial pivoting

Module 2

• Matlab: syntax and main commands
• Implementation of algorithms and methods seen in Module 1 in a Matlab environment
• Numerical solution of the heat equation starting from the methods seen in Module 1. Stationary and non-stationary heat equation
• Numerical solution of the wave equation starting from the methods seen in Module 1
• Numerical solution of the Burgers equation starting from the methods seen in Module 1

For non-attending Students: no additions to the contents indicated are necessary.

Readings/Bibliography

• Elementi di calcolo numerico, Monegato, Libreria Universitaria Levrotto e Bella
• Numerical Methods, Dukkipati, New Age International Publishers
• Numerical Analysis, Burden e Faires, Cengage Learning
• Numerical Methods for Engineers and Scientists, Hoffman, Marcel Dekker

Materials provided by the teacher. Use of interactive platforms (Teams, Virtuale) for the exchange of materials and their elaboration interacting with the teacher.

For non-attending Students: no additions to the required materials indicated in the previous points are necessary

Teaching methods

• Lectures with overhead projector and slides
• Practical exercises on Matlab
• Asynchronous teaching (refer to Teaching tools)

Assessment methods

Written test with numerical exercises and open questions on the tools and procedures to address the numerical solution of problems/models inherent to energy engineering

Teaching tools

An archive of resources (Virtual/Panopto) is available to support students in learning activities and in preparing for the exam.

The archive includes:

• teacher's notes;
• examples od flow-charts and Matlab codes;
• recordings of lectures;
• exercises to test your preparation.

Office hours

See the website of Matteo Gherardi

See the website of Pedro Vayssiere Brandão