This project follows the line of long term reserach on the development of improved discretizations for complex PDEs. Here the main focus are hyperbolic balance laws arising in many applications in physics and engineering. More particularly this project looks at so called structure preserving methods which embed genuinely discrete analogs of continuous constraints. Examples are solenoidal constraints and curl involutions, which also include he enhanced preservation of steady states, often referred to as well balanced. Other constraints as non-negativity or bounded variation within physically admissible values are also of great importance.
This work follows initial activities on the so called global flux quadrature (GFQ) approach, which has been shown to provide great enhancements in the approximation of stationary states, including multiD solenoidal constraints (for the 1d case see e.g. https://arxiv.org/abs/2212.11931 to appear on J.Comput.Phys.).
The postdoc will contribute to the investigation of several possible extensions of the approach, going from its application to more complex PDE systems, to the methodological enhancements discussed below.:
- applications of the GFQ approach to nonlinear complex multidimensional systems (Shallow Water equations, Euler equations with gravity, Maxwell equations, MHD, etc)
- development of subcell limiting strategies compatible with GFQ
- use of the GFQ strategy to enhance the solution of unsteady problems : space time formulations and ADER
- combination of GFQ with different numerical techniques: continuous and discontinuous finite elements, finite differences, finite volumes
- Entropy conservative/stable formulations
More info and application: https://recrutement.inria.fr/public/classic/en/offres/2023-06961