Intensive short course on advanced numerical methods for environmental modeling
This course on advanced numerical methods for the modeling of complex environmental processes consists of a structured intensive 2.5-week program of 80 hours 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.
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 and approximate Riemann solvers. Godunov-type and TVD finite volume methods for the shallow water equations. Asymptotic preserving staggered semi-implicit schemes for the compressible Euler and Navier-Stokes equations (all Mach number schemes) and their higher order extension via IMEX. Explicit and implicit schemes for diffusion. Implicit schemes for nonlinear parabolic equations (nonlinear heat conduction, Stefan problem, Richards’ equation). Extension to multiple space dimensions on Cartesian grids. Numerical methods for free surface flows coupled with sediment transport and permeable bottom to account for soil infiltration (shallow-water-Exner system, shallow water equations coupled with the Richards equation). Ecomorphodynamics 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
For the convenience of the non-local participants, the course will be given in a hybrid online-on-site format. The online lectures will be available via ZOOM software.
On-site, the course will be taught in room 1H of the DICAM building at Via Mesiano 77, Trento.
Fees and payment
The Master’s 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 they are planning to get from the course.
The registration fee for the course is € 216,00 and includes lecturing material and MATLAB sample codes.
How to enroll for non UniTn students
- Should you still not have a UniTn account, you have to register and log in with your SPID credential (Public Digital Identity System). If you cannot use SPID, please create your own UniTn account.
- Complete the online application Apply for enrollment in ‘Standard’ single classes a.y. 2022/2023
- In the field of "Teaching activities", please provide the following information:
- Name of single class/teaching activity Environmental modeling (or Modellistica ambientale)
- Code of single class/teaching activity 140230
- Degree course to which the teaching activity is associated 0332H
- Please wait for the outcome of the application.
- Pay the bulletin you find in Esse3 - Registrar's office - MyTasse.
- For MSc students, Ph.D. students, and post-docs of the University of Trento onsite and online participation is free.
Registration deadline is 31st March 2023 at 12:00.
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.
About Trento and the Dolomites
The historical city of Trento is situated in the autonomous Italian region of Trentino - Südtirol, close to the world-famous mountains called Dolomites. Trento is very easy to reach by car or train from Austria (150 km south of Innsbruck) and from Verona (90 km north of Verona). The nearest and most convenient airport is Verona Airport, 15 minutes from the Verona train station. The region around Trento is of extraordinary beauty, with its unique mountains and lakes that offer the participants many exciting outdoor activities like skiing, hiking, or climbing.
The course received informational support from the International Association for Hydro-Environment Engineering and Research (IAHR)