Unstructured Meshing Tools for Fusion Plasma Simulations FASTMath Team Members: Fan Zhang, Mark S. Shephard, E. Seegyoung Seol Scientific Computation Research Center, Rensselaer Polytechnic Institute S/W tools and libraries were integrated to provide meshing capability to two fusion plasma simulation codes under development at Princeton Plasma Physics Laboratory, XGC1 and M3D-C1. The meshing procedure is fully automatic with consideration of (i) physics and physical geometric components, (ii) complex meshing requirements and (iii) desired quality control with local modification. Tokamak Geometry Tokamak Geometry Meshes for XGC1 PPPL fusion plasma codes employ unstructured meshes: Specific meshing requirements focused on toroidal cross section Require automatic mesh generation and interface to parallel mesh infrastructure physics components physical components magnetic axis vacuum vessel open flux surface wall region closed flux surface plasma region XGC1 separatrix vacuum boundary *** **** scrape-off layer Parallel program to solve gyrokinetic Vlasov-Maxwell equations Tacking of ions and electrons through particle-in-cell (PIC) method Gyrokinetic Poisson equation numerically solved at the reactor scale to define fields that push particles Must account for coupling of fields and particles Particle motion is updated using Runge-Kutta 4-step iteration or 3rd order Predictor-Corrector Reactor fields are solved using a distributed unstructured mesh Mesh and particles must be properly coupled at each step in the simulation outer wall boundary plasma core inner wall boundary x point Helpful Graphic Geometric model combines physics and physical components Physics components: features interior to the reactor Flux surface is a key physics component Physical components: Tokamak design Constant flux curves are constructed Input flux (ψ) values are obtained from magnetic field on a coarse grid Interpolative splines are constructed from this data to give continuous and smooth ψ values Curves are then constructed to perpendicular to the gradient of ψ and parallel to the magnetic field, meaning each curve has a constant ψ value. [source: EPSI] Improved x-point area by controlling mesh size and element aspect ratio Meshes with different parameters for field line placement and spacing between vertices Meshes for M3D-C1 M3D-C1 Meshing Requirements Parallel solver program to study non-linear instabilities of plasmas in tokamak Solving non-linear two-fluid resistive magnetohydrodynamics (MHD) equations C1 finite element applied to solve 4th order PDEs Tools automatically support 2D to 3D linkage 3D axisymmetric: 2D mesh with real tensor field 3D analytic: 2D mesh with complex tensor field Full 3D: 3D mesh with real tensor field Common: controlling element size, shape and field lines. Requirements for XGC1 Layered mesh in critical area following field lines (flux surfaces on the cross section) with one-element deep marching strategy Mesh improvement near the x-point Unstructured mesh at the wall boundary Requirements for M3D-C1 Initial 2D mesh on the cross section Mesh adaptation on the cross section by local modification 3D distributed mesh construction (symmetric in the toroidal direction) Providing mesh data to control system assembly Slice view of 3D mesh constructed with 64 planes Mesh generated from NSTX model with a finite thickness wall 3D mesh on 12,288 procs (64 planes) Initial solution by Axisymmetric analysis (left) phi=1/2 pi (right) phi=3/2 pi Non-axisymmetric result by full 3D analysis 2D mesh (plane) on 192 procs More Information: http://redmine.scorec.rpi.edu/projects/epsi or contact Mark Shephard, RPI, shephard@rpi.edu