CSE Symposium Keynote

Paul Fischer, Argonne National Laboratory

Accurate, Stable, and Scalable Algorithms for Convection-Dominated Flows

Tuesday, April 10, 2007, 3:00 P.M.
2240 DCL, 1304 W. Springfield Ave., Urbana, IL

Abstract

Accuracy and stability have long been essential pillars of numerical algorithms for the simulation of fluid flow. With the advent of tera- and petascale parallel computers comprising thousands or hundreds of thousands of processors, scalability is emerging as another essential pillar. To first order, scalability implies that the solution time be only weakly dependent on the number of processors P, with n/P fixed, where n is the number of degrees of freedom in the problem. Time-dependent transport problems having minimal dissipation, such as electromagnetics and convection-dominated flow, face an additional scalability challenge, namely, that dispersion errors accumulated at small scales may become dominant when propagated through the large domains that are afforded by petaflops computers.

This talk will cover several critical developments that make it possible to use spectral element simulations in large-scale convection-dominated incompressible flow simulations on tens of thousands of processors. Discretization advances that have made the SEM viable for these problems include stabilizing filters and spectral element dealiasing. Solver advances include spectral element multigrid methods that employ robust Schwarz-based smoothers and scalable parallel coarse-grid solvers. In addition to these fundamental elements, we touch upon a few technical details that were required to exceed processor counts in excess of 10,000. We present the results of several spectral element simulations, including turbulent vascular flows, heat transfer in reactor core subchannels, and MHD results computed using > 100 million grid points on 32000 processors of IBM's Blue Gene Watson platform.

Biography

Dr. Paul Fischer is a computational scientist in the Mathematics and Computer Science Division of Argonne National Laboratory. He received his M.S. in mechanical engineering at Stanford and Ph.D at MIT. Before joining Argonne, he was on the applied mathematics faculty at Brown University. He has a long-standing interest in advanced scientific computing applied to flow simulation. He was co-author of the first three-dimensional spectral element code for computational fluid dynamics, which was also one of the first software products for distributed memory parallel computers. His current work is focused on development of petascale software for simulation of fluid flow and heat transfer with applications in vascular flows, ocean currents, reactor thermal-hydraulics, and astrophysics. He is the author of over 80 articles in computational fluid mechanics and co-author of the book High-Order Methods for Incompressible Fluid Flows. He was a recipient of the 1999 Gordon Bell Prize in high performance computing.

Guest speaker co-sponsored by Student Chapter of SIAM.