2026-04-13T01:42:17Zhttps://recercat.cat/oai/request

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

00925njm 22002777a 4500 dc Manyer i Fuertes, Pau author 2024-10-17 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. 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) 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