Master Internship Stability characterization of explicit-implicit high-order embedded boundary methods for linear hyperbolic systems

Description The goal of this internship is to characterize the stability of high-order embedded boundary methods within an explicit/implicit time integration framework, and to analyze the impact of boundary conditions on the global stability of the discretization. The intern will work within the PHOENICS framework and will contribute to the following activities: • Review of existing embedded boundary treatments and their stability properties, with particular attention to the Shifted Boundary method (SBM) in the Discontinuous Galerkin framework. • Analysis of linear hyperbolic systems to study how boundary conditions, and their interplay with the incoming and outgoing characteristic variables, affect the stability of the scheme. • Stability characterization comparing standard explicit and novel high-order explicit-implicit time integration strategies. • Implementation of the stability analysis in a numerical code and validation on benchmark problems. Required Skills • Background: Last year of Master’s Degree in applied mathematics, engineering, scientific computing, or related fields. • Technical skills: Numerical methods for PDEs (Finite Volume, Finite Element), programming in one or more languages (Fortran, Python, 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 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