A hybrid discontinuous Galerkin method for tokamak edge plasma simulations in global realistic geometry

Giorgiani, Giorgio; Bufferand, Hugo; Ciraolo, Guido; Ghendrih, Philippe; Schwander, F.; Serre, Éric; Tamain, P.

doi:10.1016/j.jcp.2018.07.028

Cited by 18 publications

(29 citation statements)

References 44 publications

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“…Results, which can be found in Ref. [], show the recovery of theoretical convergence rates for all the polynomial degrees tested.…”

Section: The Main Mathematical Feature Of the New Hdg Schemementioning

confidence: 81%

“…Note that, in contrast to the physical model presented by Giorgiani et al, an extra term must be taken into account to deal with non‐steady magnetic configurations. In fact, the time derivative of the plasma momentum now also accounts for the time variation of the vector b .…”

Section: Physical Modelmentioning

confidence: 99%

“…This approximation relies on the hypothesis of a slow‐varying magnetic field and the fact that the drift velocity u ⊥ produces a small effect at the diffusion values considered in the numerical experiments (see also Ref. []). Hence, the term

n \overset{true\to}{u} \cdot \partial_{t} b

is added to the formulation described by Giorgiani et al…”

Section: Physical Modelmentioning

confidence: 99%

“…A specific high‐order HDG algorithm has been developed in this study to solve this 2D model where the flow in the parallel direction corresponds to a compressible adiabatic gas flow, whereas in the perpendicular direction, it corresponds to an incompressible flow, dominated by turbulence process. All details are provided by Giorgiani et al, and only the main mathematical features are introduced here.…”

Section: The Main Mathematical Feature Of the New Hdg Schemementioning

confidence: 99%

“…With this aim, we explored the use of a high‐order hybrid discontinuous Galerkin (HDG) finite‐element method that works on unstructured, non‐aligned discretizations. This new approach has been recently detailed by Giorgiani et al, where validation tests in particular have demonstrated the ability of the new solver to discretize accurately real geometries and to extend computations up to the tokamak centre.…”

Section: Introductionmentioning

confidence: 99%

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A new high‐order fluid solver for tokamak edge plasma transport simulations based on a magnetic‐field independent discretization

Giorgiani

Camminady

Bufferand

et al. 2018

Contributions to Plasma Physics

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Our global understanding of the power exhaust in tokamaks, and its implications for both steady‐state and transient heat loads on divertor and limiter PFCs, is still poor. In transient situations in particular, such as during start‐up or control operations, the evolution of particles and heat fluxes is little known, although they are critical for the safety of the machine. The heat load is largely determined by the physics of the Scrape‐Off Layer (SOL), and therefore, it depends to a large extent on the geometry of the magnetic surfaces as well as on the geometry of wall components. A better characterization of the heat exhaust mechanisms is therefore required 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. For transient simulations, it becomes crucial to be able to deal with non‐stationary magnetic configurations. In particular, avoiding expensive re‐meshing of the computational domain is mandatory. In an attempt to achieve these goals, we propose a new fluid solver based on a high‐order hybrid discontinuous Galerkin (HDG) finite element method. Capitalizing on the experience acquired in the development of the SOLEDGE2D‐EIRENE transport model, we propose to study edge plasma transport in the frame of a reduced model (but containing most of the challenging issues regarding accurate numerical simulations) based on electron density and parallel momentum. The code is verified using manufactured solutions and validated using well‐referenced simulations in a realistic WEST geometry. Finally, we demonstrate how the particle fluxes at the wall vary in our model when the magnetic equilibrium evolves in time, particularly during the equilibrium construction skip from a limiter configuration to a diverted one at the beginning of the operation.

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“…Results, which can be found in Ref. [], show the recovery of theoretical convergence rates for all the polynomial degrees tested.…”

Section: The Main Mathematical Feature Of the New Hdg Schemementioning

confidence: 81%

Section: Physical Modelmentioning

confidence: 99%

n \overset{true\to}{u} \cdot \partial_{t} b

is added to the formulation described by Giorgiani et al…”

Section: Physical Modelmentioning

confidence: 99%

Section: The Main Mathematical Feature Of the New Hdg Schemementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A new high‐order fluid solver for tokamak edge plasma transport simulations based on a magnetic‐field independent discretization

Giorgiani

Camminady

Bufferand

et al. 2018

Contributions to Plasma Physics

Self Cite

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show abstract

Spatial adaptivity in SOLEDGE3X‐HDG for edge plasma simulations in versatile magnetic and reactor geometries

Piraccini

Schwander

Serre

et al. 2022

Contributions to Plasma Physics

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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.

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Unstructured mesh tools for magnetically confined fusion system simulations

Shephard,

Merson,

Sahni

et al. 2024

Engineering with Computers

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A hybrid discontinuous Galerkin method for tokamak edge plasma simulations in global realistic geometry

Abstract: Please cite this article in press as: G. Giorgiani et al., A hybrid discontinuous Galerkin method for tokamak edge plasma simulations in global realistic geometry, J. Comput. Phys. (2018), https://doi.

Cited by 18 publications

References 44 publications

A new high‐order fluid solver for tokamak edge plasma transport simulations based on a magnetic‐field independent discretization

A new high‐order fluid solver for tokamak edge plasma transport simulations based on a magnetic‐field independent discretization

Spatial adaptivity in SOLEDGE3X‐HDG for edge plasma simulations in versatile magnetic and reactor geometries

Unstructured mesh tools for magnetically confined fusion system simulations

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