A Gaussian-like immersed-boundary kernel with three continuous derivatives and improved translational invariance

Yuanxun Bao, Jason Kaye, Charles S. Peskin

Research output: Contribution to journalArticlepeer-review

Abstract

The immersed boundary (IB) method is a general mathematical framework for studying problems involving fluid-structure interactions in which an elastic structure is immersed in a viscous incompressible fluid. In the IB formulation, the fluid described by Eulerian variables is coupled with the immersed structure described by Lagrangian variables via the use of the Dirac delta function. From a numerical standpoint, the Lagrangian force spreading and the Eulerian velocity interpolation are carried out by a regularized, compactly supported discrete delta function, which is assumed to be a tensor product of a single-variable immersed-boundary kernel. IB kernels are derived from a set of postulates designed to achieve approximate grid translational invariance, interpolation accuracy and computational efficiency. In this note, we present a new 6-point immersed-boundary kernel that is C3 and yields a substantially improved translational invariance compared to other common IB kernels.

Original languageEnglish (US)
Pages (from-to)139-144
Number of pages6
JournalJournal of Computational Physics
Volume316
DOIs
StatePublished - Jul 1 2016

Keywords

  • Discrete delta function
  • Fluid-structure interaction
  • Immersed boundary method
  • Immersed-boundary kernel
  • Translational invariance

ASJC Scopus subject areas

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • Physics and Astronomy(all)
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics

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