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

Matthias Kirchhart, Shinnosuke Obi

研究成果: Article

抜粋

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 particle 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 experiments confirm the analysis and show that the Cartesian grid-size σ should be taken proportional to the square-root of the particle spacing h, resulting in significant speed-ups in vortex methods.

元の言語English
ページ(範囲)A2345-A2364
ジャーナルSIAM Journal on Scientific Computing
39
発行部数5
DOI
出版物ステータスPublished - 2017 1 1

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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