Giorgio Giorgiani

The simulation of fusion plasmas in realistic magnetic configurations and tokamak geometries still requires the development of advanced numerical algorithms owing to the complexity of the problem. In this context, we propose a Hybrid Discontinuous Galerkin (HDG) method to solve 2D transport fluid equations in realistic magnetic and tokamak wall geometries. This high-order solver can handle magnetic equilibrium free structured and unstructured meshes allowing a much more accurate discretization of the plasma facing components than current solvers based on magnetic field aligned methods associated with finite-differences (volumes) discretization. In addition, the method allows for handling realistic magnetic equilibrium, eventually non steady, a critical point in the modeling of full discharges including ramp up and ramp down phases. In this paper, we introduce the HDG algorithm with a special focus on recent developments related to the treatment of the cross-field diffusive terms, and to an adaptive mesh refinement technique improving the numerical efficiency and robustness of the scheme. The updated solver is verified with a manufactured solution method, and numerical tests are provided to illustrate the new capabilities of the code.

A new neutral fluid code has been developed as a necessary step towards a hybrid fluid/kinetic neutral model, to be used in ITER or DEMO simulations, where part of the divertor will be very collisional for neutrals. The neutral fluid code, which is able to handle complex geometries in view of the coupling to Soledge2D, is tested on plasma backgrounds obtained by Soledge2D‐Eirene in WEST geometry, for different divertor regimes, and is found to be in fair agreement with the kinetic Monte Carlo solver Eirene. The differences are due to the simplifications introduced in the fluid model and to the fact that a fluid description is not fully valid in these cases.

Our global understanding of the power exhaust in tokamaks, and its implications for both steady‐state and transient heat loads on divertor and limiter PFCs, is still poor. In transient situations in particular, such as during start‐up or control operations, the evolution of particles and heat fluxes is little known, although they are critical for the safety of the machine. The heat load is largely determined by the physics of the Scrape‐Off Layer (SOL), and therefore, it depends to a large extent on the geometry of the magnetic surfaces as well as on the geometry of wall components. A better characterization of the heat exhaust mechanisms is therefore required to improve the capabilities of the transport codes in terms of geometrical description of the wall components and in terms of the description of the magnetic geometry. For transient simulations, it becomes crucial to be able to deal with non‐stationary magnetic configurations. In particular, avoiding expensive re‐meshing of the computational domain is mandatory. In an attempt to achieve these goals, we propose a new fluid solver based on a high‐order hybrid discontinuous Galerkin (HDG) finite element method. Capitalizing on the experience acquired in the development of the SOLEDGE2D‐EIRENE transport model, we propose to study edge plasma transport in the frame of a reduced model (but containing most of the challenging issues regarding accurate numerical simulations) based on electron density and parallel momentum. The code is verified using manufactured solutions and validated using well‐referenced simulations in a realistic WEST geometry. Finally, we demonstrate how the particle fluxes at the wall vary in our model when the magnetic equilibrium evolves in time, particularly during the equilibrium construction skip from a limiter configuration to a diverted one at the beginning of the operation.

In the scrape-off layer (SOL) of tokamaks, the flow acceleration due to the presence of limiter or divertor plates rises the plasma velocity in a sonic regime. These high velocities imply the presence of a strong shear between the SOL and the core of the plasma that can possibly trigger some parallel shear flow instability. The existence of these instabilities, denoted as parallel Kelvin-Helmholtz instability in some works [1, 2] have been investigated theoretically in [3] using a minimal model of electrostatic turbulence composed of a mass density and parallel velocity equations. This work showed that the edge plasma around limiters might indeed be unstable to this type of parallel shear flow instabilities. In this work, we perform 3D simulations of the same simple mathematical model to validate an original finite volume numerical method aimed to the numerical study of edge plasma. This method combines the use of triangular unstructured meshes in the poloidal section and structured meshes in the toroidal direction and is particularly suited to the representation of the real complex geometry of the vacuum chamber of a tokamak. The numerical results confirm that in agreement with the theoretical expectations as well as with other numerical methods, the sheared flows in the SOL are subject to parallel Kelvin-Helmholtz instabilities. However, the growth rate of these instabilities is low and these computations require both a sufficient spatial resolution and a long simulation time. This makes the simulation of parallel Kelvin-Helmholtz instabilities a demanding benchmark.