Advanced numerical methods for environmental modeling (May 15-31, 2024)
Online and on-site (Trento, Italy) venue
Online participation is possible. The lectures and practical lessons will be recorded, and the recordings will be made available within a few minutes after each lecture ends so that the possible time difference between a student's location and Trento is not an issue.
The course is designed for MSc and PhD students, young researchers, and practitioners.
Course Overview
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 (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.
Your professors
Prof. Ilya Peshkov, Ph.D. (ilya.peshkov AT unitn.it)
Ph.D. in computational solid mechanics from the Sobolev Institute of Mathematics, 2009
Postdoctoral research positions in Canada and France
Assistant Professor, University of Trento, Italy, 2019
Associate Professor in Numerical Analysis, University of Trento, Italy, 2022
Interests: Continous fluid and solid mechanics, Numerical methods
Prof. Annunziato Siviglia, Ph.D.
Ph.D. in Modeling in Environmental Fluid Mechanics from the University of Genova, 2003
Postdoctoral research positions in Trento (Italy), 2006-2012
Senior Scientist at ETH Zurich (Switzerland), 2013-2019
Associate Professor in Hydraulics, University of Trento, Italy, 2019
Interests: River Morphodynamics, Biofluidmechanics, Numerical methods
Content (see the Program tab)
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.
Registration and administrative info
The registration deadline is 31st March 2024 at 12:00.
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
Search for the course "Environmental modeling", course ID is [140230].
Please wait for the outcome of the application (1-3 days).
Pay the bulletin you find in Esse3 - Administrative Office - Payments.
Fees
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 of € 216,00 for the 6 credits.
The registration fee includes lecturing materials, video recordings of the lectures, and MATLAB sample codes.
Exam
The exam consists of implementing a numerical method related to the course subject and writing a report (∼ 5-10 pages) containing numerical results and a short overview of the employed numerical methods.
Digital Open Badge
Upon successful completion of the course, students will be issued a Digital Badge containing detailed information about the course to certify their achievement.
You can find more info about the Open Digital Badge (ODB) by visiting this page.
Partners
We are greatful to our partners for their informational support
