Mathematics

• Introduction to CFD, examples.
• Constitutive laws
• Incompressible flows.
• Numerical methods for potential and thermal flows
• Boundary layer theory
• Thermodynamics effects, energy equation, enthalpy and entropy
• Vorticity equations
• Numerical methods for viscous flows: steady Stokes equations
• Stabilization and inf-sup condition
• Numerical methods for nonlinear viscous flows: steady Navier-Stokes equations
• Discretization techniques for steady and unsteady Navier-Stokes equations.

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.

- Introduction to the physics and applications of soft active materials: polymers, gels, natural and biological tissues
- Preliminaries (1): the Principle of Virtual Power and its consequences
- Preliminaries (2): Thermodynamics and constitutive equations: dissipation inequality and Coleman-Noll procedure
- A mechanical framework for active materials: metric description of elasticity and multiplicative decomposition of the deformation gradient

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

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