Vol.3, No.1, 2007, pp.37-48, doi:10.3970/fdmp.2007.003.037
OPEN ACCESS
ARTICLE
Non-Graded Adaptive Grid Approaches to the Incompressible Navier-Stokes Equations
  • Frédéric Gibou1, Chohong Min2, Hector D. Ceniceros3
Mechanical Engineering Department & Computer Science Department, University of California, Santa Barbara,CA 93106.
Mathematics Department, University of California, SantaBarbara, CA 93106.
Mathematics Department, University of California, SantaBarbara, CA 93106.
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.
Cite This Article
Gibou, F., Min, C., Ceniceros, H. D. (2007). Non-Graded Adaptive Grid Approaches to the Incompressible Navier-Stokes Equations. FDMP-Fluid Dynamics & Materials Processing, 3(1), 37–48.