Adaptive Hybridizable Discontinuous Galerkin discretization of the Grad–Shafranov equation by extension from polygonal subdomains

Sánchez-Vizuet, Tonatiuh; Solano, Manuel E.; Cerfon, Antoine J.

doi:10.1016/j.cpc.2020.107239

Adaptive Hybridizable Discontinuous Galerkin discretization of the Grad–Shafranov equation by extension from polygonal subdomains

Journal Article · Tue Mar 03 00:00:00 EST 2020 · Computer Physics Communications

DOI:https://doi.org/10.1016/j.cpc.2020.107239· OSTI ID:1849943

^[1]; Solano, Manuel E. ^[2]; Cerfon, Antoine J. ^[3]

New York Univ. (NYU), NY (United States). Courant Inst. of Mathematical Sciences; New York Univ. (NYU), NY (United States)
Universidad de Concepción (Chile). Dept. of Mathematical Engineering. Center for Research in Mathematical Engineering CI2MA
New York Univ. (NYU), NY (United States). Courant Inst. of Mathematical Sciences

In this work, we propose a high-order adaptive numerical solver for the semilinear elliptic boundary value problem modeling magnetic plasma equilibrium in axisymmetric confinement devices. In the fixed boundary case, the equation is posed on curved domains with piecewise smooth curved boundaries that may present corners. The solution method we present is based on the hybridizable discontinuous Galerkin method and sidesteps the need for geometry-conforming triangulations thanks to a transfer technique that allows to approximate the solution using only a polygonal subset as computational domain. Moreover, the solver features automatic mesh refinement driven by a residual-based a posteriori error estimator. As the mesh is locally refined, the computational domain is automatically updated in order to always maintain the distance between the actual boundary and the computational boundary of the order of the local mesh diameter. Numerical evidence is presented of the suitability of the estimator as an approximate error measure for physically relevant equilibria with pressure pedestals, internal transport barriers, and current holes on realistic geometries.

View Accepted Manuscript (DOE)

Research Organization:: City Univ. of New York (CUNY), NY (United States)

Sponsoring Organization:: FONDECYT; USDOE; USDOE Office of Science (SC)

Grant/Contract Number:: FG02-86ER53233

OSTI ID:: 1849943

Alternate ID(s):: OSTI ID: 1633343

Journal Information:: Computer Physics Communications, Journal Name: Computer Physics Communications Journal Issue: C Vol. 255; ISSN 0010-4655

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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