A three-dimensional electrostatic particle-in-cell methodology on unstructured Delaunay-Voronoi grids

Journal Article · Mon Jun 01 00:00:00 EDT 2009 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2009.02.003· OSTI ID:21313064

Spirkin, Anton ^[1]

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1. Mechanical Engineering Department, Worcester Polytechnic Institute, 100 Institute Road, Worcester, MA 01609 (United States)

The mathematical formulation and computational implementation of a three-dimensional particle-in-cell methodology on unstructured Delaunay-Voronoi tetrahedral grids is presented. The method allows simulation of plasmas in complex domains and incorporates the duality of the Delaunay-Voronoi in all aspects of the particle-in-cell cycle. Charge assignment and field interpolation weighting schemes of zero- and first-order are formulated based on the theory of long-range constraints. Electric potential and fields are derived from a finite-volume formulation of Gauss' law using the Voronoi-Delaunay dual. Boundary conditions and the algorithms for injection, particle loading, particle motion, and particle tracking are implemented for unstructured Delaunay grids. Error and sensitivity analysis examines the effects of particles/cell, grid scaling, and timestep on the numerical heating, the slowing-down time, and the deflection times. The problem of current collection by cylindrical Langmuir probes in collisionless plasmas is used for validation. Numerical results compare favorably with previous numerical and analytical solutions for a wide range of probe radius to Debye length ratios, probe potentials, and electron to ion temperature ratios. The versatility of the methodology is demonstrated with the simulation of a complex plasma microsensor, a directional micro-retarding potential analyzer that includes a low transparency micro-grid.

• OSTI ID: 21313064
• Journal Information: Journal of Computational Physics, Journal Name: Journal of Computational Physics Journal Issue: 10 Vol. 228; ISSN JCTPAH; ISSN 0021-9991
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGORITHMS
ANALYTICAL SOLUTION
BOUNDARY CONDITIONS
CELL CYCLE
COLLISIONLESS PLASMA
DEBYE LENGTH
DUALITY
ELECTRIC POTENTIAL
ELECTRONS
INTERPOLATION
ION TEMPERATURE
LANGMUIR PROBE
OPACITY
SENSITIVITY ANALYSIS
SIMULATION
SLOWING-DOWN
THREE-DIMENSIONAL CALCULATIONS
VALIDATION