Finite difference schemes for incompressible flows on fully adaptive grids

Frédéric Gibou, Chohong Min, Hector Ceniceros

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

2 Scopus citations


We describe a finite difference scheme for simulating incompressible flows on nonuniform meshes using quadtree/octree data structure. A semi- Lagrangian method is used to update the intermediate fluid velocity in a standard projection framework. Two Poisson solvers on fully adaptive grids are also described. The first one is cell-centered and yields first-order accurate solutions, while producing symmetric linear systems (see Losasso, Gibou and Fedkiw [15]). The second is node-based and yields second-order accurate solutions, while producing nonsymmetric linear systems (see Min, Gibou and Ceniceros [17]). A distinguishing feature of the node-based algorithm is that gradients are found to second-order accuracy as well. The schemes are fully adaptive, i.e., the difference of level between two adjacent cells can be arbitrary. Numerical results are presented in two and three spatial dimensions.

Original languageEnglish
Title of host publicationInternational Series of Numerical Mathematics
PublisherSpringer Science and Business Media Deutschland GmbH
Number of pages10
StatePublished - 2007

Publication series

NameInternational Series of Numerical Mathematics
ISSN (Print)0373-3149
ISSN (Electronic)2296-6072

Bibliographical note

Publisher Copyright:
© Birkhäuser Verlag Basel/Switzerland 2006.


  • Adaptive Grid
  • Adaptive Mesh
  • Nonsymmetric Linear System
  • Nonuniform Mesh
  • Poisson Equation


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