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Concurrent Solver for Euler Equations on the Intel Delta Oct 15


With 570 nodes with a peak performance of 32 GFLOPS, the Intel Delta at the Center for Research on Parallel Computation's Caltech site has been highly effective for several different research projects, including:

Concurrent Solver for the Euler Equations Dan Meiron, Eric Van de Velde, John Hofhaus, Paul Hardy, California Institute of Technology

This project involves the development and use of a numerical scheme to integrate two-dimensional Euler equations in an annulus. The numerical scheme will be used as a basis for high resolution simulations of inviscid and viscid fluid flows. From this simulation, researchers can examine the late-time dynamics of vortex structures that emerge due to the special nature of energy transfer in two-dimensional fluid flows. With sufficient spatial resolution provided by the use of the Delta, several issues can be investigated in the examination of these vortex structures. These issues include the mechanisms of an irreversible approach to negative temperature states in the two-dimensional flows and the nature of energy distribution at equilibrium. Several theories that have been advanced regarding these issues can now be tested with the help of the simulations being developed through this project, as the algorithms being used are well suited for use on parallel machines. In addition, axisymmetrical three-dimensional flows can be simulated by modifying these algorithms slightly. These three-dimensional flows have been of use lately to study the possible singular behavior of the three- dimensional equations of motion. A significant difference between two- dimensional and three-dimensional flow is the possibility of vortex amplification through vortex stretching. It is not yet known whether divergent vorticities can be attained in a finite time as a result of such stretching, but the computational capabilities of the Delta are providing sufficient resolution to address these issues. A third project involves the translation of the parallel algorithms described above to the Fortran M language for parallel computation. Fortran M is a dialect of Fortran 77 developed by CRPC researchers Mani Chandy and Ian Foster. The language adds a few extensions to the Fortran 77 language, allowing one to construct parallel programs in which message passing can be performed in a way which is independent of the underlying architecture. In this way it is possible to guarantee that parallel programs written in Fortran M will perform deterministically. In collaboration with Chandy and a group of undergraduate students, the group has been developing "templates" in the Fortran M language that allow one to write parallel code for various common data distributions and have all aspects of communications hidden in the low level details of the underlying template. This approach to parallel programming has the advantage that, as long as one interfaces with the data structures and utilities provided through the template, parallel programs in Fortran M appear at the source level to be more or less identical with their sequential counterparts. The group is in the process of constructing templates for several common regular data distributions used in scientific computing. The scientific problems described above both possess data distributions that are amenable to this approach. Currently, the group is implementing these codes on networks of workstations, but plans to port these codes to the high-performance SP1 machine at Argonne. ----------------------------------------------------------------------------- Reprinted with permission from the July 1993 issue of Parallel Computing Research, the newsletter of the Center for Research on Parallel Computation.

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