We describe a finite difference scheme for simulating incompressible flows on nonuniform meshes using quadtree/octree data structure. A semi- Lagrangian method is used to update the intermediate fluid velocity in a standard projection framework. Two Poisson solvers on fully adaptive grids are also described. The first one is cell-centered and yields first-order accurate solutions, while producing symmetric linear systems (see Losasso, Gibou and Fedkiw ). The second is node-based and yields second-order accurate solutions, while producing nonsymmetric linear systems (see Min, Gibou and Ceniceros ). A distinguishing feature of the node-based algorithm is that gradients are found to second-order accuracy as well. The schemes are fully adaptive, i.e., the difference of level between two adjacent cells can be arbitrary. Numerical results are presented in two and three spatial dimensions.
|Title of host publication||International Series of Numerical Mathematics|
|Publisher||Springer Science and Business Media Deutschland GmbH|
|Number of pages||10|
|State||Published - 2007|
|Name||International Series of Numerical Mathematics|
Bibliographical notePublisher Copyright:
© Birkhäuser Verlag Basel/Switzerland 2006.
- Adaptive Grid
- Adaptive Mesh
- Nonsymmetric Linear System
- Nonuniform Mesh
- Poisson Equation