Open Access

ARTICLE

Non-Graded Adaptive Grid Approaches to the Incompressible Navier-Stokes Equations

by Frédéric Gibou¹, Chohong Min², Hector D. Ceniceros³

1 Mechanical Engineering Department & Computer Science Department, University of California, Santa Barbara,CA 93106.
2 Mathematics Department, University of California, SantaBarbara, CA 93106.
3 Mathematics Department, University of California, SantaBarbara, CA 93106.

Fluid Dynamics & Materials Processing 2007, 3(1), 37-48. https://doi.org/10.3970/fdmp.2007.003.037

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.

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