PhD programmes - Science and Technology
Home > Advanced Numerical Methods for Environmental Modeling

Advanced Numerical Methods for Environmental Modeling

Lecturers: Ilya Peshkov (UNITN/DICAM), Annunziato Siviglia (UNITN/DICAM)

Timetable: 2.5 weeks intensive course May 15 – 31, 2023

For convenience of the non-local participants, the course will be giving in a mixed online-on-site format. The online lectures will be available via ZOOM software.


The course on advanced numerical methods for modeling of environmental processes consists of a structured intensive 2.5 week program of 80 hours of theoretical lectures and computer laboratory exercises on advanced numerical methods for hyperbolic and nonlinear parabolic partial differential equations with applications in environmental engineering and science. The course covers standard explicit and flux-splitting finite volume methods for hyperbolic equations, semi-implicit finite volume methods for hyperbolic and nonlinear parabolic equations, e.g. shallow water equations, sediment transport (Exner equation), solidification (icing, Stefan model), ecomorphodynamic (vegetation growth, death and mutual interaction with sediments). Special emphasis is put on practical implementation of the discussed numerical methods. The lectures on the theory will be supplemented with laboratory-based computer exercises to provide hands-on experience to all participants on the practical aspects of numerical methods for hyperbolic and parabolic problems and applications using MATLAB software. The course is primarily designed for Master and Ph.D. students in applied mathematics, engineering, physics, computer science and other scientific disciplines.


Review of basic theoretical aspects of hyperbolic conservation laws and numerical concepts for hyperbolic equations. Finite volume methods for one-dimensional systems. Godunov's method. The Riemann problem.  Approximate Riemann solvers. Godunov-type finite volume methods for non-linear systems. Explicit and implicit schemes for diffusion. Implicit scheme for nonlinear parabolic equations. Godunov and TVD schemes for shallow water equations. Semi-implicit staggered scheme for the Euler equations (all Mach number scheme). Second-order in space and time IMEX scheme for the Euler system. Semi-implicit scheme for the coupled hyperbolic-parabolic equations with nonlinear diffusion (Navier-Stokes-Stefan problem). Extension to multiple space dimensions on Cartesian grids. Semi-implicit method for sediment transport with permeable bottom (shallow-water-Exner-Richards equations). Flux-splitting method for shallow-water-Exner equations and ecomorphodynamic model with applications to sediment transport and sediment transport-vegetation interaction in rivers.


The exam consists of implementing a numerical method related to the course subject and writing a 15-20 page report containing numerical results and a short overview of the employed numerical

Fees and payment

The Master and Ph.D. students of the University of Trento are free of charge.

The external students are subjected to a tuition fee which depends on the total number of credits that you are planning to get from the course.

A minimum fee of € 216,00 is due for the first 6 credits.

For each exceeding credit you will pay an extra fee of € 30,00.

How to enroll for non UniTrento students

1. Should you still not have a UniTrento account, you have to register and login with your SPID credential (Public Digital Identity System). If you cannot use SPID, please register your own unitn account.
2. Complete the online application Apply for enrollment in ‘Standard’ single classes a.y. 2022/2023 3. Please wait for the outcome of the application.
4. Pay the bulletin you find in Esse3 - Registrar's office - MyTasse.

Additional information

All enrolled students will have access to the university license of MATLAB. Onsite participants must bring their own laptops with MATLAB installed. Online participants will receive the ZOOM link of the course only after payment of the course fee.