BLANC - Blanc

Volumes Finis pour Situations Complexes – VFSitCom

Submission summary

The aim of this project is to develop finite volume type schemes for the numerical simulation of complex situations occuring in the modelling of real life problems. Based on the recent works devoted to the conception and mathematical study of finite volume schemes for complex applications (anisotropic and heterogeneous, nonlinear, coupled, etc.), VFSitCom wishes to develop new schemes with both strong theoretical properties and efficiency in the industrial framework; our ambition is to study groundbreaking numerical tools from their mathematical bases to their practical implementation in real-world situation dealing with the above described difficulties and any other which would appear in the course of the project. We thus intend to develop methods not only capable of handling the media's anisotropy or heterogeneity, strong nonlinearities (occuring for instance through couplings) and irregular or deformed grids - some of these issues being still open despite the recent literature (see "Sample specific problems" in the projet description) -, but also which can and will be implemented with success in engineering codes for various applications, as for example those of IFP (Institut Francais du Pétrole) or CEA (Commissariat à l'Energie Atomique). Starting with Finite Volume methods is quite natural since they are widely used in the engineering applications considered in the project. But, in order to reach the objectives of VFSitCom, the members of the project will not restrict themselves to only one numerical methods for PDE, and will delve into any and all known techniques (such as Discontinuous Galerkin methods, Mimetic Finite Difference schemes, Expanded Mixed Finite Element methods, etc...; see references) in order to breach the frontiers between them and come up with a new vision of the numerical analysis of PDE.

Project coordination

Jérôme DRONIOU (Université)

The author of this summary is the project coordinator, who is responsible for the content of this summary. The ANR declines any responsibility as for its contents.



Help of the ANR 180,000 euros
Beginning and duration of the scientific project: - 36 Months

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