Simulation numérique du transport dans le plasma de bord en configuration stellarator par une méthode éléments-finis d'ordre élevé Galerkin discontinue (Thèse 2024 - 2027)
Activités
Modélisation des plasmas de fusion,
Modélisation numérique,
Méthode des éléments finis
Publications scientifiques au M2P2
2025
Marcello Capasso, Ivan Kudashev, Frédéric Schwander, Éric Serre. A h‐Adaptivity Strategy for Hybridizable Discontinuous Galerkin (HDG) Simulations of Fluid Transport Models in Tokamak Plasma. International Journal for Numerical Methods in Engineering, 2025, 126 (17), pp.e70107. ⟨10.1002/nme.70107⟩. ⟨hal-05241431⟩ Plus de détails...
The highly anisotropic, multi‐scale nature of fusion plasma simulations in tokamaks, combined with the complexity in the geometries of plasma‐facing components and magnetic equilibrium, challenges numerical schemes. They therefore require the development of advanced numerical techniques to enhance computational efficiency and enable codes to simulate realistic plasma configurations relevant to tokamak operation. This paper proposes an adaptive mesh refinement strategy (h‐Adaptivity) in the SolEdge‐HDG code for the resolution of 2D fluid‐drift Braginskii equations using the Hybrid Discontinuous Galerkin (HDG) method. The strategy is based on an oscillation indicator implemented to detect under‐resolved regions and dynamically refine the mesh, associated with an a posteriori accuracy indicator built on the local difference between the solution at order and the post‐processed one at order considered as reference. The method thus enables both refinement, where necessary, as well as coarsening in regions where the solution is smooth. Numerical results obtained with this method in realistic tokamak geometry and plasma conditions show significant reductions in computational resources and an improvement in code robustness while maintaining high accuracy, particularly in regions with steep gradients or near the sharp angles of the tokamak walls. This work highlights the potential of such ‐adaptivity technique to optimize transport simulations in realistic tokamak configurations, offering a fully automated, goal‐oriented mesh refinement strategy. In addition to optimizing the numerical cost of simulation, this strategy offers all users a fully automated means of designing a mesh in any tokamak geometry.
Marcello Capasso, Ivan Kudashev, Frédéric Schwander, Éric Serre. A h‐Adaptivity Strategy for Hybridizable Discontinuous Galerkin (HDG) Simulations of Fluid Transport Models in Tokamak Plasma. International Journal for Numerical Methods in Engineering, 2025, 126 (17), pp.e70107. ⟨10.1002/nme.70107⟩. ⟨hal-05241431⟩
Journal: International Journal for Numerical Methods in Engineering
Giacomo Piraccini, Marcello Capasso, Manuel Scotto d'Abusco, Giorgio Giorgiani, Frédéric Schwander, et al.. Recent upgrades in a 2D turbulent transport solver based on a hybrid discontinuous Galerkin method for the simulation of fusion plasma in tokamak. Fluids, 2022, ⟨10.3390/fluids7020063⟩. ⟨hal-03562497⟩ Plus de détails...
The simulation of fusion plasmas in realistic magnetic configurations and tokamak ge-1 ometries still requires the development of advanced numerical algorithms owing to the complexity 2 of the problem. In this context, we propose a Hybrid Discontinuous Galerkin (HDG) method to 3 solve 2D transport fluid equations in realistic magnetic and tokamak wall geometries. This high-4 order solver can handle magnetic equilibrium free structured and unstructured meshes allowing a 5 much more accurate discretization of the plasma facing components than current solvers based 6 on magnetic field aligned methods associated to finite-differences (volumes) discretization. In 7 addition, the method allows to handle realistic magnetic equilibrium, eventually non steady, a 8 critical point in the modelling of full discharges including ramp up and ramp down phases. In 9 this paper, we introduce the HDG algorithm with a special focus on recent developments related 10 to the treatment of the cross-field diffusive terms, and to an adaptive mesh refinement technique 11 improving the numerical efficiency and robustness of the scheme. The updated solver is verified 12 with a manufactured solution method, and numerical tests are provided to illustrate the new 13 capabilities of the code.
Giacomo Piraccini, Marcello Capasso, Manuel Scotto d'Abusco, Giorgio Giorgiani, Frédéric Schwander, et al.. Recent upgrades in a 2D turbulent transport solver based on a hybrid discontinuous Galerkin method for the simulation of fusion plasma in tokamak. Fluids, 2022, ⟨10.3390/fluids7020063⟩. ⟨hal-03562497⟩
