# Mathematics Colloquia and Seminars

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### Volume-of-fluid numerical methods for PDE's with irregular boundaries

**Optimization**

Speaker: | Phil Colella, Lawrence Berkeley Laboratory |

Location: | 693 Kerr |

Start time: | Thu, Dec 5 2002, 4:10PM |

We give an overview of a set of numerical methods being developed for solving classical PDE's in irregular geometries, or in the presence of free boundaries. In this approach, the irregular boundary is represented on a rectangular grid by specifying the intersection of each grid cell with the region on either side of the boundary. Such a description leads to natural extensions of conservative finite difference methods to the case of irregular boundaries. Some of the issues that arise include consistency and stability of such methods, methods for representing the surface geometry, and the interaction of the discretization method with the boundary conditions, particularly in the case of free boundaries. We will also present results using this approach in solving several applied PDE problems.