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 ASYMPTOTIC MODELS: we 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 and schemes, trying to exploit as much as possible the interaction between PDE and numerical analysis;
- UNIFIED ADAPTIVE SPACE-TIME-PARAMETERS VIEW: the interaction of uncertainty-quantication and parameter variation with the discretisation and modelling process is studied to construct robust adaptive discrete models, possibly allowing to reduce the overall computational cost thanks to some adaptive strategy in space and parameter space, and, if relevant/necessary, in the coupling of different models ;
- HIGH ORDER PROPERTY PRESERVING ALE DISCRETIZATIONS IN CURVED DOMAINS: the accurate treatment of the geometry is considered as part of the problem. We consider two approaches. Either the equations on conformal domains, and on high order, curved, unstructured meshes, or we will proposed high order non-conformal approaches aware of the geometrical error and embedding appropriate corrections to preserve the desired accuracy properties. A 2-field approach will be accommodated in which geometrical quantities are represented/discretized along with the flow variables, possibly within an appropriate ALE (Arbitrary Lagrangian Eulerian) formulation, naturally allowing mesh movement and time dependent adaptation. The preservation of continuous physical constraints (particular solutions, involutions) is a major concern;
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 :
- Aalborg University, Denmark
- Danish Technical University, Denmark
- DUKE University, USA
- Ecole de Technologie Superieure, Quebec
- NASA Langley, USA
- North Carolina State University, USA
- RISE, Sweden
- Università di Trento, Italy
- Università di Ferrara, Italy
- Universität Zürich, Switzerland
- SUSTech, China
Industrial relations : Airbus, BGS IT&E, BRGM, CEA, EDF, Herakles, ONERA
