Parallel adaptive infrastructure for magnetically confined fusion plasma simulations

Abstract

An automatic meshing procedure is needed by two simulation codes under development at Princeton Plasma Physics Lab, M3D-C1 and XGC1. M3D-C1 requires the mesh generated and adapted on the tokamak cross-section with the option to contain a finite-thickness wall in the domain, and the 3D mesh constructed out of 2D meshes. XGC1 requires the mesh edges aligned with the magnetic flux surfaces. The mesh is one-element deep between adjacent flux surfaces and mesh improvement is applied at the X-point(s). A geometric model including both the tokamak wall structure and the magnetic flux surfaces is introduced to reflect the meshing needs. A component-based mesh generation procedure with control parameters specified on the geometric model is developed by combining unstructured triangulation, layered mesh generation by a one-element-deep marching procedure, local mesh modification, and toroidal 2D mesh extrusion to create a 3D mesh of the full reactor.

Mesh-based needs in M3D-C1 include a procedure to form the global discrete equation, methods to estimate the simulation error, and a loop of adaptive mesh control. A mesh-adjacency based matrix assembly procedure with more efficient memory usage than the procedure using the PETSc matrix library directly is developed. The numerical conditioning of the global discrete system is improved through element-level operations. An explicit a posterior error estimator that calculates the mesh-dependent norm of the residual in the strong form is derived for the reduced MHD model under the large-aspect-ratio approximation. Software tools such as PUMI for mesh management and geometric model interfacing, APF for field management, MeshAdapt for mesh modification, PETSc for global equation solving, and Simmetrix for initial mesh generation are used to form the parallel adaptive loop in M3D-C1 .

Numerical simulations of the magnetically confined plasmas play an important rule in understanding and predicting the physics in tokamak devices. In the present study, a parallel adaptive infrastructure for the magnetically confined fusion plasma simulations is developed.