Non-graded adaptive grid approaches to the incompressible Navier-Stokes equations

Frédéric Gibou, Chohong Min, Hector D. Ceniceros

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


We describe two finite difference schemes for simulating incompressible flows on nonuniform meshes using quadtree/octree data structures. The first one uses a cell-centered Poisson solver that yields first-order accurate solutions, while producing symmetric linear systems. The second uses a node-based Poisson solver that produces second-order accurate solutions and second-order accurate gradients, while producing nonsymmetric linear systems as the basis for a second-order accurate Navier-Stokes solver. The grids considered can be non-graded, i.e. the difference of level between two adjacent cells can be arbitrary. In both cases semi-Lagrangian methods are used to update the intermediate fluid velocity in a standard projection framework. Numerical results are presented in two and three spatial dimensions.

Original languageEnglish
Pages (from-to)37-48
Number of pages12
JournalFluid Dynamics and Materials Processing
Issue number1
StatePublished - 2007


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