A Lagrangian fractional step method for the incompressible navier-stokes equations on a periodic domain

Christoph Börgers, Charles S. Peskin

Research output: Contribution to journalArticle

Abstract

In the Lagrangian fractional step method introduced in this paper, the fluid velocity and pressure are defined on a collection of N fluid markers. At each time step, these markers are used to generate a Voronoi diagram, and this diagram is used to construct finite-difference operators corresponding to the divergence, gradient, and Laplacian. The splitting of the Navier-Stokes equations leads to discrete Helmholtz and Poisson problems, which we solve using a two-grid method. The nonlinear convection terms are modeled simply by the displacement of the fluid markers. We have implemented this method on a periodic domain in the planee. We describe an efficient algorithm for the numerical construction of periodic Voronoi diagrams, and we report on numerical results which indicate that the fractional step method is convergent of first order. The overall work per time step is proportional to N log N.

Original languageEnglish (US)
Pages (from-to)397-438
Number of pages42
JournalJournal of Computational Physics
Volume70
Issue number2
DOIs
StatePublished - Jun 1987

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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