Abstract

April 3, 2006

Title: High-Resolution and Adaptive Finite-Volume Methods for Computational Fluid Dynamics
Presented by: Phil Colella, Leader, Applied Numerical Algorithms Group, Lawrence Berkeley National Laboratory

Video Podcast

Abstract

In this talk, we will discuss three design principles behind modern finite-volume methods for computational fluid dynamics.

1. The use of asymptotics to derive the fundamental time scales of the problem, and the coupling between those scales, that allow one to represent the solution to complex problems in terms of those for PDE of classical type;
2. The use of conservative discretizations on locally structured grids, and the interaction between adaptivity and well-posedness of initial / boundary value problems; and
3. The use of cut-cell representations of complex geometries, including the derivation of such geometric descriptions on a grid from CAD, image, or geophysical data.

We will illustrate these ideas with examples from a variety of applications including combustion, atmospheric fluid flows, plasma physics, and viscoelastic fluids.

Biography

Phil Colella earned his Ph.D. in mathematics from UC Berkeley and is currently leader of the Lab's Applied Numerical Algorithms Group. Both see computer modeling as a vehicle for using abstract mathematical ideas to understand real-world phenomena, such as weather and combustion.