Tonatiuh Sanchez-Vizuet: An adaptive unfitted discretization for a free boundary problem in magnetic plasma confinement

Abstract
In axisymmetric magnetic confinement fusion devices, the equilibrium configuration of a plasma is determined by the balance between the hydrostatic pressure in the fluid and the magnetic forces generated by an array of external coils and the plasma itself. The equilibrium configuration is determined by the solution to a nonlinear elliptic partial differential equation. However, since the location of the plasma is not known a priori, the domain of definition of the PDE must be determined as a problem unknown, leading to a free boundary problem.

In this talk we will discuss some aspects of an interior/exterior iterative solution strategy. The method involves the coupling of an unfitted hybridizable discontinuous Galerkin solver for the solution of the problem inside the assumed plasma domain, and a boundary integral equation solver for the solution of the exterior problem. The PDE solver incorporates h-adaptivity driven by a residual a posteriori error estimator, and the constraint that the gap between the mesh and the curved boundary must remain of the order of the local mesh diameter. This results on a nested sequence of unfitted grids that “grow”” towards the physical boundary as refinement progresses. Different aspects of this work have been done is jointly with Antoine Cerfon (Type One Energy), Nestor Sanchez (Universidad Tecnologica del Peru), Manuel Solano (University of Concepción, Chile) and Evan Toler (Argonne).