Master Internship High-order structure-preserving methods for hyperbolic PDEs on curved domains with Cartesian grids

Description The goal of this internship is to design, analyze, and implement a high-order boundary treatment for hyperbolic systems of conservation laws discretized with structure-preserving methods on embedded boundaries. The intern will work within the HOPE framework and will contribute to the following activities: • Review of existing boundary treatments and high-order structure-preserving schemes, with particular attention to the stationary-preserving global-flux formulation in the finite element setting. • Design of a high-order embedded boundary condition imposition compatible with the stationaritypreserving discretization • Numerical implementation of the method in a research code, with tests on manufactured solutions and vortex-like flows to assess high-order accuracy and the preservation of stationary states. • Comparison with standard approaches to quantify the gains in accuracy and robustness. Required Skills • Background: Last year of Master’s Degree in applied mathematics, engineering, scientific computing, or related fields. • Technical skills: Finite Element Method, numerical methods for PDEs, programming in one or more languages (Python, Fortran, Matlab, C/C++) • Language: Languages of communication can be English, French or Italian. Additional information This position is for a 5-month internship, with a flexible starting date. The internship will be supervised by Mirco Ciallella and will be carried out at the Laboratoire Jacques-Louis Lions (Université Paris Cité) situated in Paris, France (Place Aurélie Nemours, 75013). The project will be done in collaboration with Davide Torlo (Università di Roma La Sapienza, Italy) and Mario Ricchiuto (INRIA Bordeaux, France) The internship reward is about 540 euros per month (plus partial refund of transportation costs). Contact Send your application (CV, transcript, short motivation letter) to the contact person below. Mirco Ciallella mirco.ciallella@u-pariscite.fr Laboratoire Jacques-Louis Lions, Université Paris Cité, 8 Place Aurélie Nemours, 75013 Paris, France