A smooth partition of unity finite element method for vortex particle regularization

Matthias Kirchhart, Shinnosuke Obi

Research output: Contribution to journalArticlepeer-review

Abstract

We present a new class of C-smooth finite element spaces on Cartesian grids, based on a partition of unity approach. We use these spaces to construct smooth approximations of parti- cle fields, i. e., finite sums of weighted Dirac deltas. In order to use the spaces on general domains, we propose a fictitious domain formulation, together with a new high-order accurate stabilization. Stability, convergence, and conservation properties of the scheme are established. Numerical experi- ments confirm the analysis and show that the Cartesian grid-size _ should be taken proportional to the square-root of the particle spacing h, resulting in significant speed-ups in vortex methods.

Original languageEnglish
JournalUnknown Journal
Publication statusPublished - 2017 Jun 21

Keywords

  • Biot-Savart law
  • Fictitious domains
  • Particle method
  • Partition of unity finite element method
  • Smooth shape functions
  • Vortex method

ASJC Scopus subject areas

  • General

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