Simulation et comparaison avec l’expérience pour la validation de modèles de problèmes multi-échelles. – Séchelles

The scientific community can now study and simulate physical, chemical and biological phenomena with mathematical models of increasing level of complexity. However many models involving system of partial differential equations (PDEs), with a large number of unknowns as well as a large spectrum of temporal and spatial scales, are out of reach for standard numerical methods. They can not be correctly simulated and then they can not be validated by using comparison with experimental measurements. The project Séchelles has the ambition to develop a new generation of numerical methods which allows an efficient and accurate treatment of the multi-scale character of several models of reaction-convection-diffusion type systems. These new methods are based on splitting methods, adaptative mesh refinement and domain decomposition techniques. After the development of the methods, another key point is that the numerical simulations must be validated and this can only be done by comparison with experimental measurrments in realistic situations. The second ambition of the project is then to propose these comparisons in three fields of applications with a high level of present technological interest, involving naturally a multi-scale modelling : - Biology and the modelling of strokes in the brain, - Physics, in the field of high frequency, repetitively pulsed plasma, - Multi-component reacting flows with complex chemistry mechanisms.