Continuously differentiable PIC shape functions for triangular meshes

Journal Article · Wed Mar 21 04:00:00 EDT 2018 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2018.02.002· OSTI ID:1429644

Barnes, D. C. ^[1]

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1. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

In this study, a new class of continuously-differentiable shape functions is developed and applied to two-dimensional electrostatic PIC simulation on an unstructured simplex (triangle) mesh. It is shown that troublesome aliasing instabilities are avoided for cold plasma simulation in which the Debye length is as small as 0.01 cell sizes. These new shape functions satisfy all requirements for PIC particle shape. They are non-negative, have compact support, and partition unity. They are given explicitly by cubic expressions in the usual triangle logical (areal) coordinates. The shape functions are not finite elements because their structure depends on the topology of the mesh, in particular, the number of triangles neighboring each mesh vertex. Nevertheless, they may be useful as approximations to solution of other problems in which continuity of derivatives is required or desired.

• Research Organization: Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)
• Sponsoring Organization: USDOE National Nuclear Security Administration (NNSA)
• Grant/Contract Number: AC04-94AL85000; NA0003525
• OSTI ID: 1429644
• Alternate ID(s): OSTI ID: 1548579
• Report Number(s): SAND--2017-10597J; 657436
• Journal Information: Journal of Computational Physics, Journal Name: Journal of Computational Physics Vol. 362; ISSN 0021-9991
• Publisher: Elsevier
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
97 MATHEMATICS AND COMPUTING
Continuous derivative
Implicit
Particle-in-cell
Triangle mesh
Unstructured mesh