Advanced course dedicated to the Numerical Solution of Partial Differential Equations through the deal.II Finite Element Library.

Topics:

The course refers to the use of computational fluid dynamics techniques to address advanced applications in environmental, cardiovascular and industrial contexts. Each topic will be corroborated by a set of numerical examples to be performed within the open source C++ finite volume library OpenFOAM.

Mathematics Area, PhD in Mathematical Analysis, Modelling and Applications (AMMA)

Master in High Performance Computing (MHPC)

Lectures Prof Gianluigi Rozza, Tutorials coordinated by Dr Michele Girfoglio, Dr Niccolò Tonicello and Nicola Demo.

This course is meant to be complementary to the courses Numerical Solution of PDEs,  Numerical Solution of PDEs Using the Finite Element Method, and Advanced FEM Techniques.

An introduction to modern tools for collaborative science

• 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: