2026-04-17T05:43:19Zhttps://recercat.cat/oai/request

oai:recercat.cat:2117/4246082025-07-23T04:10:19Zcom_2072_1033col_2072_452951

EQUILI module in ALYA: a free-boundary GradShafranov equation solver using CutFEM Development of new EQUILI module for ALYA: implementation of a free-boundary solver for the Grad-Shafranov equation Manyer i Fuertes, Pau Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Mètodes en elements finits Magnetohydrodynamics Finite element method High performance computing Plasma Equilirium Grad-Shafranov equations Alya Framework CutFem Magnetohidrodinàmica Elements finits, Mètode dels Càlcul intensiu (Informàtica) The study of Magnetohydrodynamics (MHD) for plasma systems circulating in tokamaks is crucial for improving and developing more efficient and functional nuclear fusion reactors, advancing in the research of a new clean and sustainable source of energy. Nonetheless, MHD simulations must be provided with an initial configuration of the plasma, frequently based on the equilibrium state. The Grad-Shafranov equation models the equilibrium balancing the plasma pressure and the magnetic confinement in a nuclear reactor for an axisymmetrical plasma system, yielding as a result the poloidal magnetic flux ψ field used notably to visualise the shape of the magnetically confined plasma crosssection. Following guidelines from [1] and [2], EQUILI has been developed as a new independent and functional module inside the high performance computing (HPC) multiphysics Finite Elements (FE) code ALYA [3]. EQUILI solves for a given tokamak geometry the Grad-Shafranov equation using an iterative CutFEM solver. CutFEM is part of a branch of FE methods characterised by an unfitted computational mesh, where geometries and domains are embedded and interfaces are parametrized using level-set functions. This particular method is adapted for problems where interfaces are affected by large deformations and resizing, thus making it well-suited to address magnetically confined plasma equilibrium problems. While the tokamak’s confining magnets’ currents and positions can be individually adjusted to accommodate a variety of plasma pressure and current profiles in terms of plasma positioning and shaping, the current carried by the plasma depends directly on its cross-section shape, which at the same time is affected by the plasma current self-induced magnetic field. Due to this coupling, the problem needs to be solved using an iterative solver and having the plasma shape not fixed and free (free-boundary problem) to evolve towards the equilibrium configuration, while being constraint by its own circulating current. Therefore, the flexible and deformable nature of the plasma cross-section demands in fact the implementation of a FE method that can deal with this plasticity and must be able to easily track such changes in the plasma/vacuum interface geometry. The module was validated against several ITER equilibrium formulations and a rigorous sensibility test was performed, considering variations in the poloidal field coils’ currents conforming the axisymmetrical nuclear fusion reactor. 2024-10-17 Master thesis http://creativecommons.org/licenses/by-nc-nd/4.0/ Open Access Attribution-NonCommercial-NoDerivs 4.0 International Universitat Politècnica de Catalunya