A moving finite element model of the tokamak scrapeoff region

The scrapeoff region of a tokamak, associated with the poloidal divertor and collector plates, has been a subject of intense recent interest because it is responsible for handling a major portion of the heat load from the fusion reactions and must survive great stresses. Detailed fluid modeling has been done to optimize the design of this region, with the expectation that it is a crucial component of a practical tokamak reactor. Severe numerical problems are caused by extreme anisotropy of the plasma transport, the presence of a magnetic x-point inside the computational domain, thin boundary layers at the collector plates, and multiple time scales associated with Alfven and sound waves. The authors present a new approach based on the use of Moving Finite Elements and Graph Massage. They use an unstructured grid of triangles, providing great flexibility in fitting the complex domain in the original cylindrical coordinates. The grid automatically and dynamically adapts to the evolving solution with no reliance on the coordinate system, naturally approximating a flux coordinate system where the poloidal field is strong while relaxing to a more isotropic distribution in the neighborhood of the x-point. The elimination of the flux coordinate transformation simplifies the fluid equations, avoids the singularity at the x-point and the problem of non-orthogonal collector plates, and allows for the treatment of time-dependent magnetic fields. The adaptivity of the grid automatically refines the resolution near the plates with no human intervention. A fully implicit time step allows for efficient treatment of the multiple time scales. The Graph Massage algorithm, whose primary role is in enhancing grid adaptivity for the evolving solution, plays a role as well in the non-trivial task of initially gridding up the computational domain. Results are illustrated with 3D color movies showing the evolution of the grid and the solution