M. Scotto D’abusco, I. Kudashev, G. Giorgiani, Anna Glasser, F. Schwander, et al.. First integrated core-edge fluid simulation of ITER’s Limiter-Divertor transition with SolEdge-HDG. Nuclear Materials and Energy, 2024, pp.101750. ⟨10.1016/j.nme.2024.101750⟩. ⟨hal-04720290⟩ Plus de détails...
This work explores the Limiter-Divertor transition (L-D) during the current ramp-up of ITER's Q=10 baseline plasma scenario at various central line-integrated density n_(li) values. The analysis, based on transport simulations performed with the latest version of SoleEdge-HDG, focuses on the time evolution of heat and ion particle fluxes, revealing regions of elevated temperature on the inner wall and plasma-facing components (PFCs) despite moderate loads.The investigation also delves into the effects of perpendicular convection flux terms on density build-up, comparing different formulations and their interplay with auxiliary heating sources. Furthermore, the paper shows the impact of taking into account the evolution of the parallel neutral momentum on plasma and neutral density at the targets in the context of an ITER steady-state scenario.
M. Scotto D’abusco, I. Kudashev, G. Giorgiani, Anna Glasser, F. Schwander, et al.. First integrated core-edge fluid simulation of ITER’s Limiter-Divertor transition with SolEdge-HDG. Nuclear Materials and Energy, 2024, pp.101750. ⟨10.1016/j.nme.2024.101750⟩. ⟨hal-04720290⟩
H Bufferand, J Balbin, S Baschetti, J Bucalossi, G Ciraolo, et al.. Implementation of multi-component Zhdanov closure in SOLEDGE3X. Plasma Physics and Controlled Fusion, 2022, 64 (5), pp.055001. ⟨10.1088/1361-6587/ac4fac⟩. ⟨hal-03981783⟩ Plus de détails...
The multi-component fluid closure derived by Zhdanov (2002 Transport Processes in Multicomponent Plasma (London: Taylor and Francis)) is implemented in the fluid code SOLEDGE3X-EIRENE to deal with arbitrary edge plasma composition. The closure assumes no distinction between species such as light versus heavy species separation. The work of Zhdanov is rewritten in a matricial form in order to clearly link friction forces and heat fluxes to the different species velocities and temperature gradients.
H Bufferand, J Balbin, S Baschetti, J Bucalossi, G Ciraolo, et al.. Implementation of multi-component Zhdanov closure in SOLEDGE3X. Plasma Physics and Controlled Fusion, 2022, 64 (5), pp.055001. ⟨10.1088/1361-6587/ac4fac⟩. ⟨hal-03981783⟩
M Scotto d'Abusco, G Giorgiani, J F Artaud, H Bufferand, G Ciraolo, et al.. Core-edge 2D fluid modeling of full tokamak discharge with varying magnetic equilibrium: from WEST start-up to ramp-down. Nuclear Fusion, 2022, ⟨10.1088/1741-4326/ac47ad⟩. ⟨hal-03509800⟩ Plus de détails...
In the present work we investigate for the first time the 2D fluid transport of the plasma in WEST during an entire discharge from the start-up to the ramp-down (shot #54487). The evolution of density profile, electron and ion temperatures together with the experimental magnetic equilibrium, total current and gas-puff rate is investigated. Comparisons with the interferometry diagnostic show a remarkable overall qualitative agreement during the discharge that can be quantitative at some locations in the plasma core. If at the onset of the X-points during the ramp-up the electron heat flux is dominant at the target, present results show that the ion heat flux becomes dominant during the stationary phase of the discharge. Using a simple model for erosion, present results assess the tungsten sputtering due to deuterium ions during the start-up and ramp-up phases of the discharge and confirms the need to consider full discharge simulation to accurately treat the W source of contamination. This work also demonstrates the interest of developing magnetic equilibrium free solver including efficient time integration to step toward predictive capabilities in the future for fusion operation.
M Scotto d'Abusco, G Giorgiani, J F Artaud, H Bufferand, G Ciraolo, et al.. Core-edge 2D fluid modeling of full tokamak discharge with varying magnetic equilibrium: from WEST start-up to ramp-down. Nuclear Fusion, 2022, ⟨10.1088/1741-4326/ac47ad⟩. ⟨hal-03509800⟩
Giacomo Piraccini, Frédéric Schwander, Eric Serre, Giorgio Giorgiani, Manuel Scotto D’abusco. Spatial adaptivity in SOLEDGE3X‐HDG for edge plasma simulations in versatile magnetic and reactor geometries. Contributions to Plasma Physics, 2022, 18th International Workshop on Plasma Edge Theory in Fusion Devices September 13‐15, 2021, organized by the EPFL Swiss Plasma Center, 62 (5-6), ⟨10.1002/ctpp.202100185⟩. ⟨hal-04489377⟩ Plus de détails...
With the ultimate goal to predict plasmas heat and particle fluxes in ITER operation, more efforts are required to deal with realistic magnetic configurations and tokamak geometries. In an attempt to achieve this goal, we propose an adaptive mesh refinement method added to a fluid solver based on a high‐order hybrid discontinuous Galerkin (HDG) method. Based on unstructured meshes, this magnetic equilibrium free numerical scheme has shown promising and encouraging features to solve 2D/3D transport reduced Braginski fluid equations. To improve its numerical efficiency, a mesh refinement based on h‐adpativity is investigated. We describe here an adaptive refinement strategy on a reduced edge particle transport model based on electron density and parallel momentum. This strategy is illustrated in realistic tokamak wall geometry. Computations performed show potential gains in the required number of degrees of freedom against benchmark computations with uniform meshes, along with the potential to give an automated, goal‐oriented, mesh generation technique for edge transport simulations in 2D.
Giacomo Piraccini, Frédéric Schwander, Eric Serre, Giorgio Giorgiani, Manuel Scotto D’abusco. Spatial adaptivity in SOLEDGE3X‐HDG for edge plasma simulations in versatile magnetic and reactor geometries. Contributions to Plasma Physics, 2022, 18th International Workshop on Plasma Edge Theory in Fusion Devices September 13‐15, 2021, organized by the EPFL Swiss Plasma Center, 62 (5-6), ⟨10.1002/ctpp.202100185⟩. ⟨hal-04489377⟩
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⟩
H. Bufferand, J. Bucalossi, G. Ciraolo, G. Falchetto, A. Gallo, et al.. Progress in edge plasma turbulence modelling hierarchy of models from 2D transport application to 3D fluid simulations in realistic tokamak geometry. Nuclear Fusion, 2021, 61 (11), pp.116052. ⟨10.1088/1741-4326/ac2873⟩. ⟨hal-03377162⟩ Plus de détails...
This contribution presents the recent effort at CEA and French federation for Fusion to simulate edge plasma transport with the new code SOLEDGE3X. The latter can be used both as a 2D transport code or as a 3D turbulence code. It makes possible simulating edge plasma up to the first wall including the complex wall geometry. It also includes neutral recycling and impurity sputtering, seeding and transport. In order to improve turbulence description in transport simulation, a reduced model for turbulence intensity prediction has been derived and implemented, based on "kepsilon" like models from the neutral fluid community. Applications to a JET L-mode detached plasma and to a WEST plasma are used as illustration of the code abilities
H. Bufferand, J. Bucalossi, G. Ciraolo, G. Falchetto, A. Gallo, et al.. Progress in edge plasma turbulence modelling hierarchy of models from 2D transport application to 3D fluid simulations in realistic tokamak geometry. Nuclear Fusion, 2021, 61 (11), pp.116052. ⟨10.1088/1741-4326/ac2873⟩. ⟨hal-03377162⟩
B Luce, P Tamain, G Ciraolo, Ph Ghendrih, G Giorgiani, et al.. Impact of three-dimensional magnetic perturbations on turbulence in tokamak edge plasmas. Plasma Physics and Controlled Fusion, 2021, ⟨10.1088/1361-6587/abf03f⟩. ⟨hal-03144400⟩ Plus de détails...
The impact of resonant magnetic perturbations (RMP) on the plasma edge equilibrium and on the turbulence is investigated in a circular limited configuration. The study is based on a Braginski-based isothermal fluid model. The flow response of an unperturbed case to a small amplitude three-dimensional single mode RMP is studied and a scan in amplitude and poloidal and toroidal mode number is performed. Special attention is given when magnetic islands appear in the simulation domain on flux surfaces of rational safety factor. Results show an impact of Magnetic Perturbations (MPs) on both the plasma equilibrium and on the turbulence properties, with a deviation to the reference solution which depends on the MPs amplitude and on their wavenumbers. The impact of MPs on turbulence is however globally weaker than on the plasma equilibrium, suggesting a stabilizing effect of the MP on turbulent transport. Experimental trends are recovered such as the density pump-out and the increase of the radial electric field as well as the reorganization of the parallel velocity. The ballooning of the transport is modified under the effect of the perturbations, with a shift of the peaked poloidal region from the upper to the lower outer midplane. In the present model, the SOL width is observed decreasing in the presence of MPs. Turbulence properties are also impacted with the density fluctuations level decreasing in perturbed solutions and the intermittency is globally weakened.
B Luce, P Tamain, G Ciraolo, Ph Ghendrih, G Giorgiani, et al.. Impact of three-dimensional magnetic perturbations on turbulence in tokamak edge plasmas. Plasma Physics and Controlled Fusion, 2021, ⟨10.1088/1361-6587/abf03f⟩. ⟨hal-03144400⟩
G Giorgiani, H. Bufferand, F. Schwander, E. Serre, P. Tamain. A high-order non field-aligned approach for the discretization of strongly anistropic diffusion operators in magnetic fusion. Computer Physics Communications, 2020, 254, pp.107375. ⟨10.1016/j.cpc.2020.107375⟩. ⟨hal-02613709⟩ Plus de détails...
In this work we present a hybrid discontinuous Galerkin scheme for the solution of extremely anisotropic diffusion problems arising in magnetized plasmas for fusion applications. Unstructured meshes, non-aligned with respect to the dominant diffusion direction, allow an unequalled flexibility in discretizing geometries of any shape, but may lead to spurious numerical diffusion. Curved triangles or quadrangles are used to discretize the poloidal plane of the machine, while a structured discretization is used in the toroidal direction. The proper design of the numerical fluxes guarantees the correct convergence order at any anisotropy level. Computations performed on well-designed 2D and 3D numerical tests show that non-aligned discretizations are able to provide spurious diffusion free solutions as long as high-order interpolations are used. Introducing an explicit measure of the numerical diffusion, a careful investigation is carried out showing an exponential increase of this latest with respect to the non-alignment of the mesh with the diffusion direction, as well as an exponential decrease with the polynomial degree of interpolation. A brief assessment of the method with respect to two finite-difference schemes using non-aligned discretization, but classically used in fusion modeling, is also presented.
G Giorgiani, H. Bufferand, F. Schwander, E. Serre, P. Tamain. A high-order non field-aligned approach for the discretization of strongly anistropic diffusion operators in magnetic fusion. Computer Physics Communications, 2020, 254, pp.107375. ⟨10.1016/j.cpc.2020.107375⟩. ⟨hal-02613709⟩
Giorgio Giorgiani, H. Bufferand, G. Ciraolo, Eric Serre, P. Tamain. A magnetic-field independent approach for strongly anisotropic equations arising plasma-edge transport simulations. Nuclear Materials and Energy, 2019, 19, pp.340-345. ⟨10.1016/j.nme.2019.03.002⟩. ⟨hal-02177048⟩ Plus de détails...
A [Summary] The control of the power exhaust in tokamaks is still an open issue for the future fusion operations. The heat loads on divertor and limiter PFCs is largely determined by the physics of the Scrape-Off Layer (SOL), and therefore it depends mainly on the geometry of the magnetic surfaces and on the geometry of wall components. A better characterization of the heat exhaust mechanisms requires therefore 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. The possibility of dealing with evolving magnetic configurations becomes also critical: during start-up or control operations, for example, the evolution of particles and heat fluxes is little known, although being critical for the safety of the machine. Hence, among the new capabilities of future transport codes will be the possibility of accurately describe the reactor chamber, and the flexibility with respect the magnetic configuration. In particular, avoiding expensive re-meshing of the computational domain in case of evolving equilibrium is mandatory. In order to fulfill these requirements, in this work a fluid solver based on non-aligned discretization is used to solve the plasma-edge transport equations for density, momentum and energies. Preliminary tests on non-structured meshes and realistic geometries/physical parameters show the pertinency of this novel approach.
Giorgio Giorgiani, H. Bufferand, G. Ciraolo, Eric Serre, P. Tamain. A magnetic-field independent approach for strongly anisotropic equations arising plasma-edge transport simulations. Nuclear Materials and Energy, 2019, 19, pp.340-345. ⟨10.1016/j.nme.2019.03.002⟩. ⟨hal-02177048⟩
Giorgio Giorgiani, Hugo Bufferand, Guido Ciraolo, Philippe Ghendrih, Frédéric Schwander, et al.. A hybrid discontinuous Galerkin method for tokamak edge plasma simulations in global realistic geometry. Journal of Computational Physics, 2018, 374, pp.515-532. ⟨10.1016/j.jcp.2018.07.028⟩. ⟨hal-02114246⟩ Plus de détails...
Progressing toward more accurate and more efficient numerical codes forthe simulation of transport and turbulence in the edge plasma of tokamaks,we propose in this work a new hybrid discontinous Galerkin solver. Basedon 2D advection-diffusion conservation equations for the ion density and theparticle flux in the direction parallel to the magnetic field, the code simulatesplasma transport in the poloidal section of tokamaks, including the open fieldlines of the Scrape-off Layer (SOL) and the closed field lines of the core re-gion. The spatial discretization is based on a high-order hybrid DG schemeon unstructured meshes, which provides an arbitrary high-order accuracywhile reducing considerably the number of coupled degrees of freedom witha local condensation process. A discontinuity sensor is employed to identifycritical elements and regularize the solution with the introduction of artificialdiffusion. Based on a finite-element discretization, not constrained by a flux-aligned mesh, the code is able to describe plasma facing components of anycomplex shape using Bohm boundary conditions and to simulate the plasmain versatile magnetic equilibria, possibly extended up to the center. Nu-merical tests using a manufacturated solution show appropriate convergenceorders when varying independently the number of elements or the degree ofinterpolation. Validation is performed by benchmarking the code with thewell-referenced edge transport code SOLEDGE2D (Bufferandet al.2013,2015 [1, 2]) in the WEST geometry. Final numerical experiments show thecapacity of the code to deal with low-diffusion solutions.
Giorgio Giorgiani, Hugo Bufferand, Guido Ciraolo, Philippe Ghendrih, Frédéric Schwander, et al.. A hybrid discontinuous Galerkin method for tokamak edge plasma simulations in global realistic geometry. Journal of Computational Physics, 2018, 374, pp.515-532. ⟨10.1016/j.jcp.2018.07.028⟩. ⟨hal-02114246⟩
Giorgio Giorgiani, Hervé Guillard, Boniface Nkonga, Eric Serre. A stabilized Powell–Sabin finite-element method for the 2D Euler equations in supersonic regime. Computer Methods in Applied Mechanics and Engineering, 2018, 340, pp.216-235. ⟨10.1016/j.cma.2018.05.032⟩. ⟨hal-01865708⟩ Plus de détails...
In this paper a Powell–Sabin finite-element (PS-FEM) scheme is presented for the solution of the 2D Euler equations in supersonic regime. The spatial discretization is based on PS splines, that are piecewise quadratic polynomials with a global continuity, defined on conforming triangulations. Some geometrical issues related to the practical construction of the PS elements are discussed, in particular, the generation of the control triangles and the imposition of the boundary conditions. A stabilized formulation is considered, and a novel shock-capturing technique in the context of continuous finite-elements is proposed to reduce oscillations around the discontinuity, and compared with the classical technique proposed by Tezduyar and Senga (2006). The code is verified using manufactured solutions and validated using two challenging numerical examples, which allows to evaluate the performance of the PS discretization in capturing the shocks.
Giorgio Giorgiani, Hervé Guillard, Boniface Nkonga, Eric Serre. A stabilized Powell–Sabin finite-element method for the 2D Euler equations in supersonic regime. Computer Methods in Applied Mechanics and Engineering, 2018, 340, pp.216-235. ⟨10.1016/j.cma.2018.05.032⟩. ⟨hal-01865708⟩
Journal: Computer Methods in Applied Mechanics and Engineering
G. Ciraolo, H. Bufferand, J. Bucalossi, Ph. Ghendrih, P. Tamain, et al.. H-mode WEST tungsten divertor operation: deuterium and nitrogen seeded simulations with SOLEDGE2D-EIRENE. Nuclear Materials and Energy, 2017, 12, pp.187 - 192. ⟨10.1016/j.nme.2016.12.025⟩. ⟨hal-01702237⟩ Plus de détails...
Simulations of WEST H-mode divertor scenarios have been performed with SOLEDGE2D-EIRENE edge plasma transport code, both for pure deuterium and nitrogen seeded discharge. In the pure deuterium case, a target heat flux of 8 MW/m2 is reached, but misalignment between heat and the particle outflux yields 50 eV plasma temperature at the target plates. With nitrogen seeding, the heat and particle outflux are observed to be aligned so that lower plasma temperatures at the target plates are achieved together with the required high heat fluxes. This change in heat and particle outflux alignment is analysed with respect to the role of divertor geometry and the impact of vertical vs horizontal target plates on neutrals spreading.
G. Ciraolo, H. Bufferand, J. Bucalossi, Ph. Ghendrih, P. Tamain, et al.. H-mode WEST tungsten divertor operation: deuterium and nitrogen seeded simulations with SOLEDGE2D-EIRENE. Nuclear Materials and Energy, 2017, 12, pp.187 - 192. ⟨10.1016/j.nme.2016.12.025⟩. ⟨hal-01702237⟩
Giorgio Giorgiani, Hervé Guillard, Boniface Nkonga. A Powell-Sabin finite element scheme for partial differential equations . ESAIM: Proceedings, 2016, 53, pp.64-76. ⟨10.1051/proc/201653005⟩. ⟨hal-01377903⟩ Plus de détails...
In this paper are analyzed finite element methods based on Powell-Sabin splines, for the solution of partial differential equations in two dimensions. PS splines are piecewise quadratic polynomials defined on a triangulation of the domain, and exhibit a global C 1 continuity. Critical issues when dealing with PS splines, and described in this work, are the construction of the shape functions and the imposition of the boundary conditions. The PS finite element method is used at first to solve an elliptic problem describing plasma equilibrium in a tokamak. Finally, a transient convective problem is also considered, and a stabilized formulation is presented.
Giorgio Giorgiani, Hervé Guillard, Boniface Nkonga. A Powell-Sabin finite element scheme for partial differential equations . ESAIM: Proceedings, 2016, 53, pp.64-76. ⟨10.1051/proc/201653005⟩. ⟨hal-01377903⟩
Giorgio Giorgiani, Sonia Fernández-Méndez, Antonio Huerta. Hybridizable Discontinuous Galerkin with degree adaptivity for the incompressible Navier-Stokes equations ✩. Computers and Fluids, 2014. ⟨hal-01717504⟩ Plus de détails...
A degree adaptive Hybridizable Discontinuous Galerkin (HDG) method for the solution of the incompressible Navier-Stokes equations is presented. The key ingredient is an accurate and computationally inexpensive a posteriori error estimator based on the super-convergence properties of HDG. The error estimator drives the local modification of approximation degree in the elements and faces of the mesh, aimed at obtaining a uniform error distribution below a user-given tolerance in a given are of interest. Three 2D numerical examples are presented. High efficiency of the proposed error estimator is found, and an important reduction of the computational effort is shown with respect to non-adaptive computations, both for steady state and transient simulations.
Giorgio Giorgiani, Sonia Fernández-Méndez, Antonio Huerta. Hybridizable Discontinuous Galerkin with degree adaptivity for the incompressible Navier-Stokes equations ✩. Computers and Fluids, 2014. ⟨hal-01717504⟩
Giorgio Giorgiani, David Modesto, Sonia Fernández-Méndez, Antonio Huerta. High-order continuous and discontinuous Galerkin methods for wave problems. International Journal for Numerical Methods in Fluids, 2013, 73(10), pp.883-903. ⟨10.1002/fld.3828⟩. ⟨hal-01717513⟩ Plus de détails...
Three Galerkin methods —continuous Galerkin (CG), Compact Discontinuous Galerkin (CDG) and Hybridizable Discontinuous Galerkin (HDG)— are compared in terms of performance and computational efficiency in two-dimensional scattering problems for low and high-order approximations. The total number of degrees of freedom and the total runtime are used for this correlation as well as the corresponding precision. The comparison is carried out through various numerical examples. The superior performance of high-order elements is shown. At the same time, similar capabilities are shown for CG and HDG, when high-order elements are adopted, both of them clearly outperforming CDG.
Giorgio Giorgiani, David Modesto, Sonia Fernández-Méndez, Antonio Huerta. High-order continuous and discontinuous Galerkin methods for wave problems. International Journal for Numerical Methods in Fluids, 2013, 73(10), pp.883-903. ⟨10.1002/fld.3828⟩. ⟨hal-01717513⟩
Journal: International Journal for Numerical Methods in Fluids
