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, Elsevier, 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, Elsevier, 2019, 19, pp.340-345. ⟨10.1016/j.nme.2019.03.002⟩. ⟨hal-02177048⟩
Giorgio Giorgiani, H. Bufferand, G. Ciraolo, P. Ghendrih, Frédéric Schwander, et al.. A hybrid discontinuous Galerkin method for tokamak edge plasma simulations in global realistic geometry. Journal of Computational Physics, Elsevier, 2018, 374, pp.515-532. ⟨10.1016/j.jcp.2018.07.028⟩. ⟨hal-01946999⟩ Plus de détails...
Progressing toward more accurate and more efficient numerical codes for the simulation of transport and turbulence in the edge plasma of tokamaks, we propose in this work a new hybrid discontinuous Galerkin solver. Based on 2D advection-diffusion conservation equations for the ion density and the particle flux in the direction parallel to the magnetic field, the code simulates plasma transport in the poloidal section of tokamaks, including the open field lines of the Scrape-off Layer (SOL) and the closed field lines of the core region. The spatial discretization is based on a high-order hybrid DG scheme on unstructured meshes, which provides an arbitrary high-order accuracy while reducing considerably the number of coupled degrees of freedom with a local condensation process. A discontinuity sensor is employed to identify critical elements and regularize the solution with the introduction of artificial diffusion. Based on a finite-element discretization, not constrained by a flux-aligned mesh, the code is able to describe plasma facing components of any complex shape using Bohm boundary conditions and to simulate the plasma in versatile magnetic equilibria, possibly extended up to the center. Numerical tests using a manufactured solution show appropriate convergence orders when varying independently the number of elements or the degree of interpolation. Validation is performed by benchmarking the code with the well-referenced edge transport code SOLEDGE2D (Bufferand et al., 2013, 2015 [1,2]) in the WEST geometry. Final numerical experiments show the capacity of the code to deal with low-diffusion solutions.
Giorgio Giorgiani, H. Bufferand, G. Ciraolo, P. Ghendrih, Frédéric Schwander, et al.. A hybrid discontinuous Galerkin method for tokamak edge plasma simulations in global realistic geometry. Journal of Computational Physics, Elsevier, 2018, 374, pp.515-532. ⟨10.1016/j.jcp.2018.07.028⟩. ⟨hal-01946999⟩
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, Elsevier, 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, Elsevier, 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, Elsevier, 2018, 340, pp.216-235. 〈hal-01947259〉 Plus de détails...
In this paper a Powell-Sabin finite-element (PS-REM) 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 C-1 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. (C) 2018 Elsevier B.V. All rights reserved.
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, Elsevier, 2018, 340, pp.216-235. 〈hal-01947259〉
Journal: Computer Methods in Applied Mechanics and Engineering
Matteo Valentinuzzi, Giorgio Giorgiani, Yannick Marandet, Hugo Bufferand, Guido Ciraolo, et al.. Fluid description of neutral particles in divertor regimes in WEST. Contributions to Plasma Physics, Wiley-VCH Verlag, 2018, 58 (6-8), pp.710-717. ⟨10.1002/ctpp.201700211⟩. ⟨hal-02116176⟩ Plus de détails...
A new neutral fluid code has been developed as a necessary step towards a hybrid fluid/kinetic neutral model, to be used in ITER or DEMO simulations, where part of the divertor will be very collisional for neutrals. The neutral fluid code, which is able to handle complex geometries in view of the coupling to Soledge2D, is tested on plasma backgrounds obtained by Soledge2D‐Eirene in WEST geometry, for different divertor regimes, and is found to be in fair agreement with the kinetic Monte Carlo solver Eirene. The differences are due to the simplifications introduced in the fluid model and to the fact that a fluid description is not fully valid in these cases.
Matteo Valentinuzzi, Giorgio Giorgiani, Yannick Marandet, Hugo Bufferand, Guido Ciraolo, et al.. Fluid description of neutral particles in divertor regimes in WEST. Contributions to Plasma Physics, Wiley-VCH Verlag, 2018, 58 (6-8), pp.710-717. ⟨10.1002/ctpp.201700211⟩. ⟨hal-02116176⟩
M. Valentinuzzi, Giorgio Giorgiani, Y. Marandet, H. Bufferand, G. Ciraolo, et al.. Fluid description of neutral particles in divertor regimes in WEST. Contributions to Plasma Physics, Wiley-VCH Verlag, 2018, 58 (6-8), pp.710-717. ⟨hal-01947244⟩ Plus de détails...
A new neutral fluid code has been developed as a necessary step towards a hybrid fluid/kinetic neutral model, to be used in ITER or DEMO simulations, where part of the divertor will be very collisional for neutrals. The neutral fluid code, which is able to handle complex geometries in view of the coupling to Soledge2D, is tested on plasma backgrounds obtained by Soledge2D-Eirene in WEST geometry, for different divertor regimes, and is found to be in fair agreement with the kinetic Monte Carlo solver Eirene. The differences are due to the simplifications introduced in the fluid model and to the fact that a fluid description is not fully valid in these cases.
M. Valentinuzzi, Giorgio Giorgiani, Y. Marandet, H. Bufferand, G. Ciraolo, et al.. Fluid description of neutral particles in divertor regimes in WEST. Contributions to Plasma Physics, Wiley-VCH Verlag, 2018, 58 (6-8), pp.710-717. ⟨hal-01947244⟩
L. Valade, A. Ekedahl, P. Ghendrih, Y. Sarazin, Y. Asahi, et al.. Electron burst driven by near electric field effects of lower-hybrid launchers. Contributions to Plasma Physics, Wiley-VCH Verlag, 2018, 58 (6-8), pp.465-470. ⟨hal-01947214⟩ Plus de détails...
Hotspot generation by lower-hybrid (LH) launchers is found to be governed by a resonance in the plasma electric field response to the external drive. The kinetic analysis in 1D-1V in the parallel direction allows one to compute the amplification effect for small amplitude of the external drive. The resonant Lorentzian response distorts the distribution function. An island structure is formed in the suprathermal part at the phase velocity of the external electrostatic drive. The non-linear features enhance the plasma response, driving overlap effects between multiple waves at rather low amplitude. The onset of a plateau in the distribution function, with extent reaching one thermal velocity, is already obtained when the standard overlap condition is achieved. The sensitivity of the resonance to plasma parameters and large variation of the amplification magnitude can compensate the fast radial decay of the small-scale features generated by the LH launchers, which are responsible for the interaction with the cold electrons. This mechanism can trigger hotspot generation further in the scrape-off layer than otherwise expected.
L. Valade, A. Ekedahl, P. Ghendrih, Y. Sarazin, Y. Asahi, et al.. Electron burst driven by near electric field effects of lower-hybrid launchers. Contributions to Plasma Physics, Wiley-VCH Verlag, 2018, 58 (6-8), pp.465-470. ⟨hal-01947214⟩
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, Elsevier, 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, Elsevier, 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, Elsevier, 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, Elsevier, 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, EDP Sciences, 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, EDP Sciences, 2016, 53, pp.64-76. ⟨10.1051/proc/201653005⟩. ⟨hal-01377903⟩
H Guillard, M Bilanceri, C Colin, Philippe Ghendrih, G Giorgiani, et al.. Parallel Kelvin-Helmholtz instability in edge plasma. Journal of Physics: Conference Series, IOP Publishing, 2014, Joint Varenna-Lausanne International Workshop 2014, 561, pp.012009. ⟨10.1088/1742-6596/561/1/012009⟩. ⟨hal-01100365⟩ Plus de détails...
In the scrape-off layer (SOL) of tokamaks, the flow acceleration due to the presence of limiter or divertor plates rises the plasma velocity in a sonic regime. These high velocities imply the presence of a strong shear between the SOL and the core of the plasma that can possibly trigger some parallel shear flow instability. The existence of these instabilities, denoted as parallel Kelvin-Helmholtz instability in some works [1, 2] have been investigated theoretically in [3] using a minimal model of electrostatic turbulence composed of a mass density and parallel velocity equations. This work showed that the edge plasma around limiters might indeed be unstable to this type of parallel shear flow instabilities. In this work, we perform 3D simulations of the same simple mathematical model to validate an original finite volume numerical method aimed to the numerical study of edge plasma. This method combines the use of triangular unstructured meshes in the poloidal section and structured meshes in the toroidal direction and is particularly suited to the representation of the real complex geometry of the vacuum chamber of a tokamak. The numerical results confirm that in agreement with the theoretical expectations as well as with other numerical methods, the sheared flows in the SOL are subject to parallel Kelvin-Helmholtz instabilities. However, the growth rate of these instabilities is low and these computations require both a sufficient spatial resolution and a long simulation time. This makes the simulation of parallel Kelvin-Helmholtz instabilities a demanding benchmark.
H Guillard, M Bilanceri, C Colin, Philippe Ghendrih, G Giorgiani, et al.. Parallel Kelvin-Helmholtz instability in edge plasma. Journal of Physics: Conference Series, IOP Publishing, 2014, Joint Varenna-Lausanne International Workshop 2014, 561, pp.012009. ⟨10.1088/1742-6596/561/1/012009⟩. ⟨hal-01100365⟩
Giorgio Giorgiani, Sonia Fernández-Méndez, Antonio Huerta. Hybridizable Discontinuous Galerkin with degree adaptivity for the incompressible Navier-Stokes equations ✩. Computers and Fluids, Elsevier, 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, Elsevier, 2014. ⟨hal-01717504⟩