Mathematics

• Introduction to CFD, examples.
• Constitutive laws
• Incompressible flows.
• Numerical methods for potential and thermal flows
• Boundary layer theory

Lectures Prof Gianluigi Rozza, Tutorials coordinated by Dr Giovanni Stabile,  Dr Francesco Ballarin, Dr Maria Strazzullo and Dr Federico Pichi

Learning outcomes and objectives

The course aims to provide the basic aspects of numerical approximation and efficient solution of parametrized PDEs for computational mechanics problem (heat and mass transfer, linear elasticity, viscous and potential flows) using reduced order methods.

All lectures are live in Room A-134, and broadcasted on Zoom and YouTube.

https://sissa-it.zoom.us/j/81471012769?pwd=QnNiZnVtbUxvNENybXlPNWVsT1hmQT09

Meeting ID: 814 7101 2769

Passcode: GitRules

Course material: https://github.com/luca-heltai/collaborative-science-2021-2022

Course description

The course deals with a list of advanced topics in computational fluid dynamics. In the first part, the governing equations governing fluid dynamics problems are reviewed and derived. Both compressible and incompressible flows are considered. The basics of the finite volume methods for the numerical discretization of fluid dynamics problems are reviewed and discussed starting from the basic example of an advection-diffusion equation.

• Reminders on linear algebra and tensor calculus
• Kinematics of deformable bodies
• Eulerian and Lagrangian descriptions of motion
• Balance laws of continuum mechanics: conservation of mass, balance of linear and angular momentum, energy balance and dissipation inequality
• Constitutive equations
• Fluid dynamics: the Navier Stokes equations
• Solid mechanics: nonlinear and linearized elasticity
• Selected topics from the mechanics of biological systems

 Books: