@Article{fdmp.2007.003.037,
AUTHOR = {Frédéric  Gibou, Chohong  Min, Hector D.  Ceniceros},
TITLE = {Non-Graded Adaptive Grid Approaches to the Incompressible Navier-Stokes Equations},
JOURNAL = {Fluid Dynamics \& Materials Processing},
VOLUME = {3},
YEAR = {2007},
NUMBER = {1},
PAGES = {37--48},
URL = {http://www.techscience.com/fdmp/v3n1/24228},
ISSN = {1555-2578},
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 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.},
DOI = {10.3970/fdmp.2007.003.037}
}