Continuously differentiable PIC shape functions for triangular meshes

JOURNAL OF COMPUTATIONAL PHYSICS

卷:362

Article

Barnes, D. C.^1,2 

[1] Sandia Natl Labs, POB 5800,Mail Stop 0878, Albuquerque, NM 87185 USA

[2] Coronado Consulting, Lamy, NM 87540 USA

关键词: Particle-in-cell;    Unstructured mesh;    Triangle mesh;    Implicit;    Continuous derivative;   

DOI  :  10.1016/j.jcp.2018.02.002

来源: Elsevier

【 摘 要 】

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. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free