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CARDAMOM Research team

Certified Adaptive discRete moDels for robust simulAtions of CoMplex flOws with Moving fronts

Team presentation

From PDEs to certified computational models : this is the motto of CARDAMOM . We aim at providing a robust model development methodology, as well as a quantitative approach to model certication, allowing to assess the robustness of the model w.r.t. each of its components (equations, numerical methods, etc), and to assess the variability of the outputs w.r.t. random variations of the data.

We will achieve this objective working toward a unified set of tools for the engineering analysis of complex  flows involving moving fronts.  Examples of such flows be found in civil, industrial, and aerospace engineering : industrial hazards (explosions), free surface hydraulics (coastal hydrodynamics, floods, etc), energy conversion facilities (gas-vapour, liquid-vapour systems, wave energy conversion, etc.), space-reentry (chemically reacting fronts, ablating walls, rarefied/continuous  flows), wing de anti-icing systems (ice-air flow),  etc.

 

Simulating, optimising, and controlling these systems in a robust manner is far from being a simple task, especially in a real life. There is still a large number of open scientic challenges. These are  related to the intrinsic nature of these flows necessitating:

  • an approppriate PDE formulation taking into account the physics relevant to the engineering applciations while remaining computationally affordable in an operational context;
  • efficient adaptive discretizations allowing to optimize the computational effort, while providing a sharp and accurate resolution of the physics;
  • a certification step quantifying the uncertainty in engineering oputputs due to all modelling choices, both physical, and mathematical (continuous and discrete)

To develop a robust and accurate model means to be able to quantify and control the effects of the choices made in each of the above steps. The development of robust models taylored to the applications mentione above is the objective of CARDAMOM.

Research themes

We will work on new formulations and re-formulations of techniques allowing to obtain numerical models for these engineering applications. Our main conviction is that appropriate modelling  has to involve a  strong coupling between PDE analysis, numerical discretisation, uncertainty quantification, and specific issues related to the engineering applications considered.  The key of the team's originality and scientific impact is the interaction of four ideas :

 

1) 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;

2) 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;

3) 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 ;

4) 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 tacke real life applciations, these four elements will be combined with a massively parallel implementation taking into account the heterogenous nature of modern computer architectures.

International and industrial relations

International relations :
  • Universität Zürich
  • von Karman Institute for Fluid Dynamics
  • Université Libre de Louvain
  • Stanford University
  • ENSAM Paris
  • Ecole Centrale Lyon
  • Nottingham University
  • Chalmers University
  • Danish Technical University
  • Politecnico di Milano
  • Ecole de Techoligie Superieure, Quebec
Industrial relations :
  • World competitivity cluster AESE
  • Dassault, Airbus, Safran, Herakles
  • ONERA
  • EDF
  • CEA