A Hybridizable Discontinuous Galerkin solver for the Grad–Shafranov equation

Sánchez-Vizuet, Tonatiuh; Solano, Manuel E.

doi:10.1016/j.cpc.2018.09.013

Title: A Hybridizable Discontinuous Galerkin solver for the Grad–Shafranov equation

Journal Article · Fri Sep 28 00:00:00 EDT 2018 · Computer Physics Communications

DOI:https://doi.org/10.1016/j.cpc.2018.09.013· OSTI ID:1610077

^[1]; Solano, Manuel E. ^[2]

New York Univ. (NYU), NY (United States)
Univ. de Concepción (Chile)

In axisymmetric fusion reactors, the equilibrium magnetic configuration can be expressed in terms of the solution to a semi-linear elliptic equation known as the Grad–Shafranov equation, the solution of which determines the poloidal component of the magnetic field. When the geometry of the confinement region is known, the problem becomes an interior Dirichlet boundary value problem. We propose a high order solver based on the Hybridizable Discontinuous Galerkin method. The resulting algorithm (1) provides high order of convergence for the flux function and its gradient, (2) incorporates a novel method for handling piecewise smooth geometries by extension from polygonal meshes, (3) can handle geometries with non-smooth boundaries and x-points, and (4) deals with the semi-linearity through an accelerated two-grid fixed-point iteration. The effectiveness of the algorithm is verified with computations for cases where analytic solutions are known on configurations similar to those of actual devices (ITER with single null and double null divertor, NSTX, ASDEX upgrade, and Field Reversed Configurations).

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Research Organization:: New York Univ. (NYU), NY (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: FG02-86ER53233

OSTI ID:: 1610077

Alternate ID(s):: OSTI ID: 1635825

Journal Information:: Computer Physics Communications, Vol. 235; ISSN 0010-4655

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 10 works

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Discontinuous Galerkin approximations in computational mechanics: hybridization, exact geometry and degree adaptivity Giacomini, Matteo; Sevilla, Ruben arXiv https://doi.org/10.48550/arxiv.1908.06604	text	January 2019
A priori and a posteriori error analysis of an unfitted HDG method for semi-linear elliptic problems Sánchez, Nestor; Sánchez-Vizuet, Tonatiuh; Solano, Manuel E. arXiv https://doi.org/10.48550/arxiv.1911.12298	preprint	January 2019
A parallel cut-cell algorithm for the free-boundary Grad-Shafranov problem Liu, Shuang; Tang, Qi; Tang, Xian-Zhu arXiv https://doi.org/10.48550/arxiv.2012.06015	preprint	January 2020

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70 PLASMA PHYSICS AND FUSION TECHNOLOGY
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Title: A Hybridizable Discontinuous Galerkin solver for the Grad–Shafranov equation

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