1. 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
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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: or contact Mark Shephard, RPI,