Speaker
Description
Fluid transport simulations based on mean-field quantities, with the averaged out turbulence fluctuations being modelled, remain a standard in the international community when considering engineering studies of tokamak relevant configurations (for a review of state-of-the-art transport codes, see Schwander et al. 2024).
In the perspective of enhancing computational efficiency and expanding codes capabilities, we started developing SOLEDGE-HDG, a high-order, finite-element code within the SOLEDGE code suite approximately ten years ago [Giorgiani et al. 2018 ; Capasso et al. 2025].
The hybridization of the DG method enables a special choice of the numerical traces (or numerical fluxes) for spatial discretization, which makes the HDG stand out thanks to its stability features, reduced number of degrees of freedom, and super-convergence properties (the error converges faster than the degree of the polynomials used to represent approximate the solution) [Giorgiani et al. 2018]. The innovation of this HDG method for tokamak simulations lies in its mesh flexibility which eliminates the need for alignment with magnetic field lines or flux surfaces. This enables accurate discretization of complex plasma-facing components and singularities (e.g., X-points) as well as the simulation of non-steady phases (e.g., start-up) without costly remeshing, addressing a gap left by current codes. Relieving the constraint of aligment with magnetic field comes at the price of additional spurious numerical diffusion in the perpendicular direction that can be bounded as long as high-order interpolations are used [Giorgiani et al. 2020]. The HDG scheme also promotes implicit time integration that relies on rapid Newton-Raphson convergence, thus allowing large time steps and fast computational access to steady states, leading to superior performance of SOLEDGE-HDG in achieving 2D transport equilibria when compared to semi-implicit codes.
In this presentation, we will detail the algorithm, highlighting both its attractive properties and its current limitations. Over recent years, the code has been successfully applied to simulate tokamak-relevant configurations [Scotto et al. 2022, Kudashev et al. 2026]. Selected results will be presented to illustrate the code’s new capabilities and its strong potential for addressing transport and heat exhaust challenges in existing devices, as well as in next-generation machines such as ITER [Scotto et al. 2024] or SPARC.