Dirichlet boundary conditions for arbitrary-shaped boundaries in stellarator-like magnetic fields for the Flux-Coordinate Independent method
详细信息 查看全文
- 作者：Peter Hill ; Peter.Hill@york.ac.uk ; Brendan Shanahan ; Ben Dudson
- 关键词：Plasma ; Stellarator
- 刊名：Computer Physics Communications
- 出版年：2017
- 出版时间：April 2017
- 年：2017
- 卷：213
- 期：Complete
- 页码：9-18
- 全文大小：1444 K
- 卷排序：213
文摘
We present a technique for handling Dirichlet boundary conditions with the Flux Coordinate Independent (FCI) parallel derivative operator with arbitrary-shaped material geometry in general 3D magnetic fields. The FCI method constructs a finite difference scheme for ∇∥∇∥ by following field lines between poloidal planes and interpolating within planes. Doing so removes the need for field-aligned coordinate systems that suffer from singularities in the metric tensor at null points in the magnetic field (or equivalently, when q→∞q→∞). One cost of this method is that as the field lines are not on the mesh, they may leave the domain at any point between neighbouring planes, complicating the application of boundary conditions.The Leg Value Fill (LVF) boundary condition scheme presented here involves an extrapolation/interpolation of the boundary value onto the field line end point. The usual finite difference scheme can then be used unmodified. We implement the LVF scheme in BOUT++ and use the Method of Manufactured Solutions to verify the implementation in a rectangular domain, and show that it does not modify the error scaling of the finite difference scheme. The use of LVF for arbitrary wall geometry is outlined.We also demonstrate the feasibility of using the FCI approach in nonn-axisymmetric configurations for a simple diffusion model in a “straight stellarator” magnetic field. A Gaussian blob diffuses along the field lines, tracing out flux surfaces. Dirichlet boundary conditions impose a last closed flux surface (LCFS) that confines the density. Including a poloidal limiter moves the LCFS to a smaller radius.The expected scaling of the numerical perpendicular diffusion, which is a consequence of the FCI method, in stellarator-like geometry is recovered. A novel technique for increasing the parallel resolution during post-processing, in order to reduce artefacts in visualisations, is described.