Research Activity

My research work has been dealing with mathematical models and numerical methods for numerical simulation aimed at problem solving in fluid dynamics, material science, cultural heritage, planetology and environmental sciences.

Mathematical Models approached are listed:

- Navier-Stokes equations for unsteady, incompressible, non-isothermal fluids (Direct Numerical Simulation, Large Eddy Simulation, stability analysis and dynamical systems)

- incompressible non-newtonian fluid models (power law, differential type, Glen’s law)

- liquid/solid phase transition models with convection and deformation (artificial crystal growth, icy satellites of the solar system, subglacial lakes in polar regions)

- convection/diffusion equations for aqueous solutions with ionic chemical species

- bio-fluid dynamics for the plankton ecosystem (natural surfactant effects).

Numerical Methodologies adopted are the following:

- finite differences and finite volumes methods

- spectral and B-spline polynomial approximation methods

- domain decomposition technique

- front-fixing and front-tracking technique for moving boundary problems

- regular and singular perturbation methods