### Abstract

Considers the fractional step method, and studies problems involving immersed boundaries in which the boundaries are modelled by a chain of Lagrangian particles connected by springs. Adapts the algorithm for the construction of Voronoi meshes for the case of a periodic domain, noting possible use of the Delauney triangulation. Proves that the discrete divergence and gradient operators are weakly consistent with the corresponding continuous operators. Describes a two level iteration for the solution of discrete Helmholtz equations and presents a vector field on to its divergence free part. Finally, obtains a fractional step method for the Navier-Stokes equations. (C.J.U.)

Original language | English (US) |
---|---|

Title of host publication | Unknown Host Publication Title |

Publisher | Springer-Verlag |

Edition | (eds.), Berlin, Fed. Rep. Germany, Springer-Verlag, 1985, p.8... |

ISBN (Print) | 3540159924, 9783540159926 |

State | Published - Jan 1 1985 |

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### ASJC Scopus subject areas

- Engineering(all)

### Cite this

*Unknown Host Publication Title*((eds.), Berlin, Fed. Rep. Germany, Springer-Verlag, 1985, p.8... ed.). Springer-Verlag.

**A Lagrangian method based on the Voronoi diagram for the incompressible Navier Stokes equations on the periodic domain.** / Borgers, C.; Peskin, Charles.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

*Unknown Host Publication Title.*(eds.), Berlin, Fed. Rep. Germany, Springer-Verlag, 1985, p.8... edn, Springer-Verlag.

}

TY - CHAP

T1 - A Lagrangian method based on the Voronoi diagram for the incompressible Navier Stokes equations on the periodic domain.

AU - Borgers, C.

AU - Peskin, Charles

PY - 1985/1/1

Y1 - 1985/1/1

N2 - Considers the fractional step method, and studies problems involving immersed boundaries in which the boundaries are modelled by a chain of Lagrangian particles connected by springs. Adapts the algorithm for the construction of Voronoi meshes for the case of a periodic domain, noting possible use of the Delauney triangulation. Proves that the discrete divergence and gradient operators are weakly consistent with the corresponding continuous operators. Describes a two level iteration for the solution of discrete Helmholtz equations and presents a vector field on to its divergence free part. Finally, obtains a fractional step method for the Navier-Stokes equations. (C.J.U.)

AB - Considers the fractional step method, and studies problems involving immersed boundaries in which the boundaries are modelled by a chain of Lagrangian particles connected by springs. Adapts the algorithm for the construction of Voronoi meshes for the case of a periodic domain, noting possible use of the Delauney triangulation. Proves that the discrete divergence and gradient operators are weakly consistent with the corresponding continuous operators. Describes a two level iteration for the solution of discrete Helmholtz equations and presents a vector field on to its divergence free part. Finally, obtains a fractional step method for the Navier-Stokes equations. (C.J.U.)

UR - http://www.scopus.com/inward/record.url?scp=85040859692&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85040859692&partnerID=8YFLogxK

M3 - Chapter

SN - 3540159924

SN - 9783540159926

BT - Unknown Host Publication Title

PB - Springer-Verlag

ER -