This proposal regards the study and the development of a new class of numerical methods to simulate natural or laboratory plasmas and in particular magnetic fusion processes. In this context, we aim in giving a contribution, from the mathematical, physical and algorithmic point of view, to the ITER project.
We remark that, nowadays, we still lack of numerical schemes which are able to simulate both efficiently and correctly these complex phenomena. This is essentially due to the great difficulties in simulating the different time and space scales involved in these problems. For our project, we propose to join together different teams which will cover the different aspects of the same problem. These teams will take advantage of the strong experience already acquired in this field.
In details, for our project, we propose a collaboration between the Mathematical Department of the Toulouse University IMT, the Mathematical Department of the Marseille University LATP with the scope of analyzing the models and design appropriate numerical methods, the CEA/IRFM for the definition of the relevant physical models and their application and the INRIA Toulouse to furnish the indispensable support for the algorithmic part and the coding development.
The scope of the project is to join the competences of different teams and to pose the bases for a new methodology of plasma simulations. In the current state-of-the-art, specialized codes for specific plasma phenomena (i.e. turbulence, waves, fast particles, impurities, MHD) and/ or for the various plasma regions (the core, the edge, the divertor, etc. ) are available and a lot of effort is done in the coupling of these codes one to each other. However, the results often depend on the coupling strategies which results of the lack of robustness of the schemes and in predictions. In addition, many models are constrained with meshes along the magnetic field, which often implies the necessity to adapt the geometry to the mesh and makes the methods not very versatile. ITER is a 25 years project and, in a decade or two from now, the available computer power will allow global simulations of the full device. Our goal is to prepare the numerical algorithms which will be needed to face this challenge.
In more details, the core of this project consists in the development, the analysis, the implementation and the testing on real physical problems of the so-called Asymptotic-Preserving methods which allow simulations over a large range of scales with the same model and numerical method. These methods represent a breakthrough with respect to the state-of-the art. They will be developed specifically to handle the various challenges related to the simulation of the ITER plasma.
In parallel with this class of methodologies, we intend to design appropriate coupling techniques between macroscopic and microscopic models for all the cases in which a net distinction between different regimes can be done. This will permit to describe different regimes in different regions of the machine with a strong gain in term of computational efficiency, without losing accuracy in the description of the problem.
We will then establish open source software libraries for the simulation of plasmas that can be described by kinetic or fluid equations. In particular we will develop full 3-D solver for the asymptotic preserving fluid as well as kinetic model. The Asymptotic-Preserving (AP) numerical strategy allows us to perform numerical simulations with very large time and mesh steps and leads to impressive computational saving. These advantages will be combined with the utilization of the last generation preconditioned fast linear solvers to produce a software with very high performance for plasma simulation.