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Summary: Copyright c 2007 Tech Science Press FDMP, vol.3, no.1, pp.37-48, 2007
Non-Graded Adaptive Grid Approaches to the Incompressible
Navier-Stokes Equations
Frédéric Gibou 1, Chohong Min 2, Hector D. Ceniceros 3
(Communicated by John Lowengrub and Mark Sussman)
Abstract: 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 Pois-
son solver that yields first-order accurate solu-
tions, 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 dif-
ference of level between two adjacent cells can be
arbitrary. In both cases semi-Lagrangian methods
are used to update the intermediate fluid velocity
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