Below are listed some possible projects. These are initially intended to be master projects but, after some additional discussions, can perhaps also be reduced to become semester projects.
If you are interested in one of these projects, please contact the primary on the project to discuss details.
You are always welcome to contact the chair if you have specific interests that we can then explore to see how they match with ongoing activities.
Fractional modeling of sediment transport in the bay of Venice
The objective of this project is to investigate the applicability range of the memory functions formalism to intertidal sediment transport in morphologically and hydro-dynamically complex lagoons, such as the Venice lagoon. The memory of the system is specifically described by the Caputo formalism involving fractional time derivatives. Such formalism applies to the basic constitutive relation for intertidal transport. This is inferred from replicated outcomes of long-term simulations by detailed mathematical and numerical models.
This is an active research topic which provides the candidate with a chance for original work. Furthermore, the project is of interdisciplinary nature and offers an opportunity for active collaboration with people in hydrology and environmental sciences from both EPFL and the University of Padua, Italy.
The project requires expertise in different areas. The candidate will need to acquire basic knowledge of fractional calculus, and understand numerical schemes for the approximation of fractional differential equations. The project will involve a non-trivial coding component which will require to implement the time fractional scheme within the framework of an existing finite element code. Depending on the timeframe, the project may involve simulations for different geometrical settings, including some of notable morphological complexity.
Primary contact: Paolo Gatto
2D adaptive WENO methods based on RBF reconstructions
Essentially Non-Oscillatory (ENO) and the more recent Weighted ENO (WENO) methods, together with a suitable time integrating method, are used to solve hyperbolic conservation laws. Arbitrary high order and stability of these methods received considerably attention for their efficiency in capturing singularities of the solution, such as sharp gradients and shock fronts. Notwithstanding the popularity of these methods, they are limited to uniform grids because they rely on polynomial reconstruction.
Recently, Radial Basis Functions (RBFs) have been used as an alternative to polynomials in the WENO reconstruction step. This class of functions are typically used to approximate func- tions given an arbitrary collection of points, thus making them suitable for reconstructions on both structured and unstructured meshes. The generalization to non-polynomial interpolation overcomes the restriction to equidistant grids and allows for mesh adaptation, which is necessary to keep a good balance between the required accuracy and the computational complexity.
The goal of this project is to study and implement a 2D adaptive RBF-WENO method for systems of nonlinear conservation laws and test it on the benchmark Euler equations. Key topics to be considered include a suitable choice of RBF, a stencil selection strategy, an r-Adaptation approach and related choice of error estimators, and possibly an extension to fully unstructured meshes. The method has already been developed by members of the MCSS Chair in 1D and the candidate will be provided with an existent Matlab code, which will have to be extended.
Primary contact: Caterina Bigoni