The goal is the design of highly efficient simulation methods of fluid models for plasmas and particularly, plasma turbulence in Tokamaks. The state-of-the-art consists in using drift-fluid models i.e. fluids models subject to the hypothesis that the plasma gyro-frequency is large compared to the typical time scale of the phenomena of interest. However, it is desirable to go beyond the drift-fluid approximation and to use the unaltered balance equations for each particle species. Indeed, the drift-approximation does not permit to follow the regimes where the magnetic field lines are locally and dynamically altered by the coupling with the plasma.
Specifically, this project explores the methodology of Asymptotic-Preserving (AP) schemes which allows one to switch automatically between two models related by an asymptotic theory. This technology avoids the drawbacks of model coupling strategies, in which the two models are coupled through a coupling region or an interface. Here, the AP property guarantees that the scheme automatically shifts from the gyro-fluid model to the standard Euler equations when the gyro-frequency becomes larger. The design and implementation of such ‘Gyro-scale asymptotic-preserving schemes’, is the goal of the present research programme.
Another, but related, goal of this project is to make the method effective in arbitrary coordinate systems or mesh geometries compared to the magnetic geometry. In this way, the method is able to treat cases where the magnetic field geometry or topology evolves in the course of time. The development of these new techniques may generate considerable impact by producing large computational savings and increased robustness and reliability of the simulations with a wider range of applicability.