FEM-BEM coupling methods for Tokamak plasma axisymmetric free-boundary equilibrium computations in unbounded domains

Abstract

Incorporating boundary conditions at infinity into simulations on bounded computational domains is a repeatedly occurring problem in scientific computing. The combination of finite element methods (FEM) and boundary element methods (BEM) is the obvious instrument, and we adapt here for the first time the two standard FEM-BEM coupling approaches to the free-boundary equilibrium problem: the Johnson-Nédélec coupling and the Bielak-MacCamy coupling. We recall also the classical approach for fusion applications, dubbed according to its first appearance von-Hagenow-Lackner coupling and present the less used alternative introduced by Albanese, Blum and de Barbieri in [2]. We show that the von-Hagenow-Lackner coupling suffers from undesirable non-optimal convergence properties, that suggest that other coupling schemes, in particular Johnson-Nédélec or Albanese-Blum-de Barbieri are more appropriate for non-linear equilibrium problems. Moreover, we show that any of such coupling methods requires Newton-like iteration schemes for solving the corresponding non-linear discrete algebraic systems.

Automating the design of tokamak experiment scenarios

“…We refer to [9,Chapter 2.4] for the details of the derivation. Alternative approaches, that incorporate the boundary conditions at infinity were recently presented in [7]. Quadrature rules.…”

“…In the beginning (first three pictures) the plasma touches the limiter and becomes more and more elongated (limiter configuration) while finally, it moves into the divertor configuration, where the plasma boundary contains an X-point of the poloidal flux. with (7) µ[ ](r, z) = µ f (|r (r, z)| 2 r 2 )…”

An overview of the numerical methods for tokamak plasma equilibrium computation implemented in the NICE code

“…The current density in these structures is then computed as a function of the input voltages in the PF circuits and/or of the time derivative of the poloidal ux (dened below) as shown in Eqs. (11) and (12) below. We refer to standard text books (e.g.…”

Finite element methods on composite meshes for tuning plasma equilibria in tokamaks

“…The bilinear form c(•, •) [2,11,18] takes into account the boundary conditions at infinity using Greens functions of the operator -∇ • ( 1 μx r ∇(•)). It is defined as follows…”

“…The elements of P2-Q3 are not only continuous on in h and ex h but have also continuous gradients on in h . We focus on the overlapping MEM-M (10) which uses the modified mortar mappings and is equivalent to (11). We also analyze the influence on the error curves of using either L 2 projections or interpolation to realize the gluing across γ ex and γ in for the MEM-M. We start with the case where in h has minimal overlap with ex h (see Fig.…”