The work on the C-90 has been completed and a paper entitled "A Vector-Parallel Scheme for Navier Stokes Computations at Multi-Gigaflop Performance Rates" has been submitted to The International Journal on Numerical Methods in Fluids. Here we describe the domain decomposition strategy and time-stepping recursion algorithm that led to better than 8-Gigaflop/s sustained performance rates for NSFLOW on the C-90.
In spring Alfred and Dr. Carey participated in the UT Austin CHPC Cray-Day meeting and gave a presentation entitled "Multi-gigaflop Performance for Navier-Stokes Problems on Cray Supercomputers." Here, Dr. Carey first gave an overview on the relationship between computational fluid dynamics and supercomputing. Alfred then detailed the work he has done on the Y-MP and C-90, including the 8 Gigaflops/s performance results. A video illustrating the algorithm's performance and flow solution was also shown. This video was prepared jointly with Andrew Wissink at Cray. Some of this work was also covered in the paper "Cray Y-MP C-90 Results for NSFLOW" presented to Cray as part of our 1993 Cray R&D Grant year end report.
One of the novel features in our algorithm work involves a class of time-stepping recursions as the basis of an iterative solution scheme. The basic idea is to modify the 4-stage Runge-Kutta family to optimize the stability domain and yield a recursion that converges to the steady state solution more rapidly. This algorithm has been designed to vectorize and parallelize well. In July Alfred attended the 14th IMACS World Congress on Computational and Applied Mathematics and gave a presentation on the algorithm research entitled "Iterative Runge-Kutta on Parallel Supercomputers". The presentation included some of the C-90 results for the parallel Runge-Kutta algorithms we have developed. The talk was accompanied by the paper entitled "Time-Iterative Recursion with Domain Decomposition for Viscous Flows" which appears in Proceedings of the 14th IMACS World Congress on Computation and Applied Mathematics, July 11-15, 1994, Georgia Institute of Technology, Atlanta, GA.
Our work in supercomputing in general, and on Cray supercomputers in particular, was also showcased in two resent editions of the UT Austin CHPC (now the High Performance Computing Facility, or HPCF) Outlook magazine. In the Spring 1994 edition (Volume 2, No. 2) in the article entitled "Engineering Design with Supercomputers" I give an overview of engineering design on supercomputers and describe some of the design work taking place in the CFDLab. In the Fall 1994 (Volume 3, No. 1) edition in the article entitled "Parallel Iterative Methods for Scalable Mathematical Libraries" I discuss the software challenges encountered when developing iterative solvers on supercomputers. Both articles include flow visualizations computed by Alfred as part of the Cray research effort.
In November 1994 Alfred and Spencer Swift attended the week long Cray short course "CRAY T3D Applications Programming" held in Houston. As a result of this course both Alfred and Spencer have been modifying their Navier-Stokes solvers to run on the T3D using the CRAFT programming model. Alfred has already made some preliminary calculations on the T3D as part of the new Cray project and soon will be performing benchmark studies. Enclosed are two plots of an early solution. The first is a plot of Stream Function contours for a Re=500 solution of flow through a curving channel. The second is a detail of the later half of the channel showing velocity vectors. In both plots the areas of separation can be clearly seen.
