## Thursday July 28/10:30/Grande Ballroom

Invited Presentation 9

**Chair: John B. Bell, Lawrence Livermore National Laboratory**
# Adaptive Numerical Methods for Partial Differential Equations

Adaptive methods are techniques for concentrating computational effort where it is most needed as a function of space, time and data. In this talk, we will discuss two classes of adaptive methods: local mesh refinement, and volume-of-fluid representations of moving free boundaries, such as discontinuities and irregular solid body geometries. In the particular approach we are taking, there are several unifying design principles. We wish to couple these methods to logically rectangular discretizations of the underlying differential equations; to minimize both the CPU and memory overhead of working with irregular data structures, preferably restricting them to a set one dimension lower than the dimension of the problem; and to maintain discrete conservation form. We will present calculations performed in two and three dimensions using various combinations of algorithms based on these ideas.
**Phillip Colella, Department of Mechanical Engineering, University of California, Berkeley**

Phillip Colella received his A.B. (1973), M.A. (1976) and Ph.D. (1979) degrees from the University of California, Berkeley, all in applied mathematics. Dr. Colella spent six years as a staff scientist at the Lawrence Berkeley Laboratory, and from 1986 to 1989 was the Group Leader for the Applied Mathematics Group at the Lawrence Livermore National Laboratory. He is currently a Professor in the Mechanical Engineering department at University of California, Berkeley. Dr. Colella's research interests are principally concerned with the development of advanced numerical algorithms for solving fluid dynamics problems, and the application of such algorithms in the investigation of fundamental phenomena in fluid dynamics, and in support of large-scale engineering applications. He is a recipient of a PYI award from the National Science Foundation.