Hill, Peter Alec orcid.org/0000-0003-3092-1858, Shanahan, Brendan William and Dudson, Benjamin Daniel orcid.org/0000-0002-0094-4867 (2016) Dirichlet boundary conditions for arbitrary-shaped boundaries in stellarator-like magnetic fields for the Flux-Coordinate Independent method. Computer Physics Communications. pp. 1-10. ISSN 0010-4655
Abstract
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 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→∞). 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 the error scaling of the finite difference scheme isn't modified. The use of LVF for arbitrary wall geometry is outlined. We also demonstrate the feasibility of using the FCI approach in non-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 is also described.
Metadata
Item Type: | Article |
---|---|
Authors/Creators: |
|
Copyright, Publisher and Additional Information: | © 2017 Elsevier B.V. This is an author-produced version of the published paper. Uploaded in accordance with the publisher’s self-archiving policy. Further copying may not be permitted; contact the publisher for details. |
Keywords: | physics.plasm-ph |
Dates: |
|
Institution: | The University of York |
Academic Units: | The University of York > Faculty of Sciences (York) > Physics (York) |
Depositing User: | Pure (York) |
Date Deposited: | 04 Jan 2017 12:13 |
Last Modified: | 03 Nov 2024 01:19 |
Status: | Published online |
Refereed: | Yes |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:110086 |