Towards nonaxisymmetry; initial results using the Flux Coordinate Independent method in BOUT++

Abstract

Fluid simulation of stellarator edge transport is difficult due to the complexities of mesh generation; the stochastic edge and strong nonaxisymmetry inhibit the use of field aligned coordinate systems. The recent implementation of the Flux Coordinate Independent method for calculating parallel derivatives in BOUT++ has allowed for more complex geometries. Here we present initial results of nonaxisymmetric diffusion modelling as a step towards stellarator turbulence modelling. We then present initial (non-turbulent) transport modelling using the FCI method and compare the results with analytical calculations. The prospects for future stellarator transport and turbulence modelling are discussed.

Fluid simulations of plasma filaments in stellarator geometries with BSTING

“…A Poincaré plot showing the flux surfaces calculated in Zoidberg is shown in figure 1. Figure 2 illustrates that simulating a parallel diffusion model qualitatively reveals the flux surfaces for a rotating ellipse equilibrium, recovering the results from [11,12]however this result differs in that it uses fully three dimensional metric tensor components, whereas the previous results utilized a metric tensor that varied in only two dimensions. It is perhaps worth mentioning that in initial testing the addition of variation in the third dimension has increased calculation time by about 5%-15%, so calculations do not require prohibitively more resources relative to conventional BOUT+ +simulations.…”

“…where b is the magnetic field vector. Here the diffusion model in equation (1) is used to test the numerical diffusion in a rotating ellipse equilibrium as done in [11,12]. Specifically, we will simulate this model on a rotating ellipse geometry.…”

“…The recent implementation of the flux coordinate independent (FCI) [10] method for parallel derivatives in BOUT+ +has allowed for simulations in non-axisymmetric geometries [11,12]. Instead of aligning the computational grid to magnetic field lines, the FCI method uses interpolation of field line mapping on poloidal (or, in the case of linear geometries, azimuthal) planes to obtain values for finite-difference differentiation parallel to the magnetic field.…”

“…Additionally, since the computational grid is no longer aligned to the magnetic field, the simulation of complex geometries including X-points is possible. For a more complete discussion of the FCI method, see [10][11][12].…”

The effects of non-uniform drive on plasma filaments

“…While BOUT++ is capable of simulating complex geometries [3][4][5], one can often explore complex phenomena by simplifying the problem. For this reason, isolated filament simulations in slab geometries are often employed [6][7][8].…”