We will work on new formulations and re-formulations of techniques allowing to obtain improved numerical models for applications in aeronautic, coastal, and industrial engineering. Our main conviction is that appropriate modelling  has to involve a  strong coupling between the specific know how of the engineering field under consideration, PDE analysis, numerical discretisation, and possibly uncertainty quantification.  So we will consider  the interaction of four ideas :

  • DISCRETE ASYMPTOTICS: we will reverse the classical modelling paradigm by proposing asymptotic variants of discretised forms of the relevant full models  (e.g. 3d Euler or Navier-Stokes). We will use this approach as a workhorse to produce new models, as well as new numerical methods, trying to exploit as much as possible the interaction between PDE and numerical analysis;
  • A UNIFIED SPACE-TIME-PARAMETERS SETTING: uncertainty-quantication techniques will be embedded in the discretisation process to allow the construction of adaptive techniques coupling spatial, temporal, and parametric domains. Our ambition is to be able to reduce the overall computational cost, by keeping a very low error level thanks to the possibility of a coupled adaptive representation in physical and parameter space;
  • HIGH ORDER GEOMETRICALLY DYNAMIC DISCRETE SETTING: from the start, the geometry of the problem is considered as part of the mathematical model. Equations will be written for the high order moving, curved, unstructured mesh, and for the  flow, with a coupling involving engineering  flow variables, or outputs related to the approximation in parameter space  (uncertainty quantisation step). This 2-field approach will be accommodated  with an appropriate ALE (Arbitrary Lagrangian Eulerian) formulation, and will allow naturally for time dependent mesh movement ;
  • OPTIMIZED APPROXIMATION AND ADAPTIVITY: We will investigate strategies to reduce the size and complexity of the representation of the  flow both in physical and in parameter space.  Two mainavenues will be explored: classical methods involving polynomial  or mesh adaptation,  more recent methods allowing to get information concerning the most important parameters,  using sensitivity analysis, or the active subspace of an approximation kernel, etc.

To tackle real life applications, these four elements will be combined with parallel implementation possibly taking into account the heterogenous nature of modern computer architectures.


International relations :

  • Universität Zürich, Switzerland (R. Abgrall)
  • Aalborg University, Denmark (C. Eskilsson)
  • Danish Technical University, Denmark (A.P. Engsig-Karup)
  • University of Nottingham, UK (M.E. Hubbard)
  • Politecnico di Milano, Italia (A. Guardone)
  • Ecole de Technologie Superieure, Quebec (F. Morency)
  • NASA Langley, USA (A. Mazaheri)
  • DUKE University, USA (G. Scovazzi)
  • North Carolina State University, USA (A. Chertock)
  • SUS Tech, China (A. Kurganov)


Industrial relations :

  • World competitivity cluster AESE
  • Dassault, Airbus, Safran, Herakles
  • EDF
  • CEA
  • BRGM

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