Advanced Numerical Methods for Environmental Modelling

Course Information

Date:             29 September – 15 October 2025 (80 hours, 30 hours/week, 6 hours a day)

Format:       Onsite and Online venue. The lectures and coding sessions will be recorded.   

Fee:                UniTn students      – free of charge. 

    External students – 216 EUR (includes video recordings, lecture notes, codes)

ECTS:            6 credits 

Audience:  Master and PhD students, young researchers, and practitioners.

UPDATE:   The detailed Program is now available (see the Program Tab)

Brief Overview

This course on advanced numerical methods for the modeling of complex environmental processes consists of a structured intensive 2.5-week (30 hours/week) program of 80 hours (6 credits) of theoretical lectures and computer laboratory exercises. The focus is on advanced numerical methods for coupled nonlinear hyperbolic and parabolic partial differential equations with applications in environmental engineering and science. The course covers explicit and flux-splitting finite volume methods for hyperbolic equations, semi-implicit finite volume methods for hyperbolic and nonlinear parabolic equations, in particular the shallow water equations with sediment transport (shallow water Exner system), nonlinear heat conduction with phase change and moving fronts (icing and deicing, Stefan problem), the Richards equation for the description of variably saturated flows in porous media and its coupling with free surface flows to study infiltration into the soil from first principles, the compressible Navier-Stokes equations and their weakly compressible limit for the description of atmospheric flows as well as eco-morphodynamics (vegetation growth, death and mutual interaction with sediments). Special emphasis is put on the 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's and Ph.D. students in applied mathematics, engineering, physics, computer science, and other scientific disciplines.

 Teachers