TY  - EJOU
AU  - Gibou, Frédéric  
AU  - Min, Chohong  
AU  - Ceniceros, Hector D.  

TI  - Non-Graded Adaptive Grid Approaches to the Incompressible Navier-Stokes Equations
T2  - Fluid Dynamics \& Materials Processing

PY  - 2007
VL  - 3
IS  - 1
SN  - 1555-2578

AB  - 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.
KW  - 

DO  - 10.3970/fdmp.2007.003.037