The course introduces fundamental concepts and techniques for the numerical modeling of engineering problems in solid and fluid mechanics. Topics will be presented through practical examples, followed by theoretical insights. By its nature, the course fosters synergy between Mechanics, Mathematics, Numerical Analysis, and Programming to solve complex engineering problems.
Knowledge and Understanding
By the end of the course, students should demonstrate knowledge and understanding of key concepts and fundamental principles of numerical techniques for solving thermo-fluid dynamics and structural problems.
Applying Knowledge and Understanding
Students should be able to:

Identify a physical model describing thermo-fluid dynamics and structural phenomena.
Associate a numerical model with the physical model.
Assess advantages and disadvantages of the resulting physical-mathematical model in terms of computational complexity, implementation, parameter acquisition, and accuracy.
Identify the main characteristics of the numerical method (stability, accuracy, etc.).
Develop an algorithm to solve the numerical model.
Graphically represent and critically interpret the obtained results.

Making Judgements
Students should demonstrate the ability to apply acquired knowledge to the analysis of practical examples.
Communication Skills
Homework assignments will assess the ability to apply learned concepts to solve simple engineering problems. The written exam will verify understanding of theoretical fundamentals.
Learning Skills
Upon completion, students should demonstrate the minimum knowledge, skills, and competences outlined in this syllabus.

Essential prerequisites:
Calculus I and II, Geometry, Physics I (Mechanics).
Recommended prerequisites:
Fluid Mechanics or Hydraulics, Thermodynamics and Heat Transfer, Structural Mechanics.

1. Initial value problems.
2. Applications: rigid body dynamics, with specific examples in naval architecture.
3. Boundary value problems and eigenvalue problems.
4. Numerical solution of parabolic, elliptic, and hyperbolic partial differential equations (PDEs).
5. Overview of numerical methods for solving Euler and Navier–Stokes equations.
6. Basic finite element method (FEM) applications in statics of deformable systems.

1. Numerical Methods For Engineering Application di J.H. Ferziger. Wiley Edrs.
* Computational FLuid Mechanics
1. Computational Fluid Dynamics di J.D. Anderson. McGraw-Hill Education
* Finite Elements
1. The Finite Element Method: Its Basis and Fundamentals di O.C. Zienkiewicz, R.L. Taylor e J.Z. Zhu. BH Edrs.
* Rigid body motion:
1. Course teaching material, Available through Teams platform
2. Goodman, L.E., Warner, W.H., 2001. Dynamics. Dover Publications Inc.

Numerical solution of ordinary differential equations (ODEs) (IVP and BVP).
Definition of fundamental equations and numerical techniques for modeling the dynamics of a rigid body (in the plane and in space), whether constrained or not.
Applications relevant to Naval Architecture (e.g., rolling motion).
Numerical techniques for solving partial differential equations (PDEs), including finite difference, finite volume, and finite element methods.
Basic finite element method (FEM) applications in statics of deformable systems (e.g., lattice structures, simple beam systems).

Lectures and practical exercises to be carried out individually or in groups, followed by collective review and discussion in class. Practical sessions will include programming tasks and numerical simulations.

NONE

Written exam with open and closed questions, including theoretical topics and practical exercises. Duration: 2 hours.

This course explores topics closely related to one or more goals of the United Nations 2030 Agenda for Sustainable Development, particularly SDG 9 (Industry, Innovation and Infrastructure) and SDG 13 (Climate Action), by promoting advanced engineering solutions and sustainable design practices.