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BACCHUS Research team

Parallel tools for Numerical Algorithms and Resolution of essentially Hyperbolic problems

  • Leader : Mario Ricchiuto
  • Research center(s) : CRI Bordeaux - Sud-Ouest
  • Field : Applied Mathematics, Computation and Simulation
  • Theme : Numerical schemes and simulations

Team presentation

The aim of this team-project is to develop and validate numerical methods adapted to physical problems modeled by a set of partial differential equations having mathematical properties that are, in most of the computational or physical domain, dictated by hyperbolic terms. This type of equations is what denote by essentially hyperbolic PDEs. in the rest of the text, though this wording is quite non standard. A typical example is that of the Navier Stokes equations in fluid dynamics for very high Reynolds numbers: in most of the domain, the viscous effects are weak, except near the solid boundaries. Our aim is to make contributions in the numerical approximation of these PDEs from the point of view of accuracy and efficiency so that very large scale computations will become much easier in the coming years. Our main focus will be on fluid dynamics applications, which are at the core of our know how and of our current research directions, but a priori the techniques developed can be applied to other models having a similar mathematical structure, such as aeroacoustics, geophysics or magneto--hydrodynamics (MHD) flows, like in the ITER project, or elastodynamics. Since the partial differential equations (PDE) involved in all these applications have similar properties, its approximation is of similar mathematical nature. The emergence of new types of massively parallel machines allowing true real size simulations, as well as the increasing demand of the industry, have led today to the following trends in numerical simulation:
  • higher accuracy is sought, especially for unsteady problems;
  • higher efficiency simulation tools for unsteady problems are or need to be developped;
  • an increase in the required level of complexity of the geometry, including a wide range of different length scales, and of the physical models, eventually including coupling of different physics and multi-scale modelling;
  • an effort is under way to try to take into account in the simulations the uncertainties in the physical model, or/and the geometry, or/and in other parameters, in order to evaluate an average behavior, variance and other statistical quantities if needed.
This list is certainly not exhaustive. It is essential to have methods which are simple to code and to run on modern high performance computers. The choice we have made here aims at {answering to all these challenges of modern scientific computing: accuracy, simplicity, flexibility. A large part of the proposal will be supported by the ADDECCO ERC advanced grant proposal which has been accepted in 2008 and has started in december 2008.

Research themes

Our objective is to provide original contributions to the numerical approximations required to tackle the above-mentioned algorithmic challenges. We do not expect to bring contributions to the physical modeling (i.e. the step from physics to PDEs and their analysis), nor to the extensive simulations of these problems in order to have a deep understanding of the physics of one given problem or of a class of problems. Once a physical model is set up, our focus will be its numerical approximation, and the way this approximation can be efficiently implemented on modern architectures. The team works on :
  • the numerical approximation of essentialy hyperbolic problems by residual distribution type methods
  • isogeometric analysis in the context of residual distribution methods
  • meshes generation of high order schemes,
  • uncertainty quantification for fluid flows,
  • graph and mesh partitionning for compressible high order sechmes
  • efficient and scalable parallel methods for large non linear problems.

International and industrial relations

    International relations
  • von Karman Institute
  • Université Libre de Louvain
  • Stanford University
  • ENSAM Paris
  • Institut National Polytechnique de Grenoble
  • Sandia Albuquerque
    Industrial relations
  • World competitivity cluster AESE
  • Dassault, Airbus, Turboméca
  • SNECMA (Haillan, Vernon, Villaroche)

Keywords: Fluid mechanics Algorithms Mesh and graph partitionning Mesh generation Parallel solution of large linear and non linear systems