April 15-17

Abstract Details

files Add files

Abstracts

Author: Tonatiuh Sanchez-Vizuet
Requested Type: Poster
Submitted: 2019-02-21 17:12:17

Co-authors: M.E. Solano, A.J. Cerfon

Contact Info:
Courant Institute of Mathematical Sciences
251 Mercer Street
New York, NY   10012
USA

Abstract Text:
We introduce a high order adaptive numerical solver for the Grad-Shafranov equation. The proposed solution procedure is based on the hybridizable discontinuous Galerkin method and builds an approximation to the solution by reformulating the problem as a first order system.

The reformulation ensures high order of approximation for the partial derivatives of the stream function and allows for the use of an unfitted triangulation of the confinement region, thus sidestepping the need for high order geometry-conforming triangulations or isoparametric mappings. This is achieved through the use of a consistent procedure to transfer the boundary conditions between the boundaries of the computational and physical domains.

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 maintain the distance between the actual boundary and the computational boundary always of the order of the local mesh diameter.

We present numerical evidence of the efficiency and reliability of the estimator and of the convergence properties of the solution in challenging configurations such as steep pressure pedestals and transport barriers in geometries with and without x-points.

Comments: