Applications
Principal Investigator: Erik Asphaug (University of California, Santa Cruz)
Co-Investigator: Kevin Olson (The University of Chicago)
High spatial resolution is required to model the shapes, discontinuities, free surfaces, and narrow shocks associated with hypervelocity impacts into solids. Another limiting dimension is time: impact simulations frequently run out of computer resources just as their behavior begins to get interesting. For these reasons, the development of massively parallel machines such as the CRAY T3E, and codes that can make effective use of them, are leading the way towards a better understanding of:
Our objective is to develop the best codes in the world for this area of research and to use them to solve previously unsolvable problems central to planetary science.
Our Smooth Particle Hydrodynamics (SPH) algorithm with strength and fracture (Benz and Asphaug 1994, 1995) has opened several fruitful avenues of planetary impact research (Asphaug et al. 1996; Asphaug 1997, 1998). However, current simulations on high-end workstations are limited to ~100,000 particles and require months of machine time to model a few seconds of evolution. We have therefore ported our smooth particle hydrocode (which includes strength and brittle fracture) onto the CRAY T3E, using the parallel tree code of Olson and Packer (1996) for the domain decomposition and neighbor search. (Domain decomposition is the algorithm for spreading "work" onto the array of processors; this must be done in an efficient, balanced manner, so as to minimize communication among processors. The neighbor search is central to any SPH method, for each particle at any time must know details regarding the ~50 or so particles closest to it.)
Our code implements a brittle fracture model within a continuum hydrocode and has been shown to reproduce the actual fragment shapes, sizes, and velocities associated with laboratory impact experiments in geologic materials. It remains the only code to date to have evolved to this level of success. At coarse resolution, our failure model yields accurate results for fragment size, provided resolution is adequate to resolve the shock causing the disruption. At higher resolutions, our method yields explicit fragments (contiguous regions of intact material bounded by interconnected failed regions, or cracks) that match the coarse-resolution results quite well, indicating that our method scales independently of code resolution. This was not the case for earlier methods (e.g. Melosh et al. 1992). Flaw statistics must be independent of resolution if high-resolution supercomputing solutions are to have any significance.
An efficient hierarchical tree lies at the heart of any large-scale N-body gravity calculation, since it reduces the N*N computation of gravitational forces to N*logN, where N is the number of particles involved in the calculation. Tree codes are also frequently employed in the rapid finding of near-neighbor particles for the SPH method. The other method is a linked list, which is somewhat faster (Hockney and Eastwood 1981; Benz and Asphaug 1995) but useless for gravity. The entire code uses the Cray SHMEM library for data transferal between processors, a library that has recently been ported to SGI multiprocessor systems, HPVM, and MPI2.
The new code, called ESPH, includes subroutines for strength (Libersky and Petschek 1990), impact fracture (Benz and Asphaug 1994, 1995), and simple plastic yielding, together with artificial viscosity for handling shocks, and N-body self gravity. ESPH has passed all of its initial tests on the CRAY T3E, including scaling benchmarks and comparisons with prior simulations. On 512 processors we have achieved a factor of 1,000 speed-up over the Principal Investigator's high-performance desktop workstation, so that a run that previously required months of patience is now completed overnight!
The benchmarks for scaling are as shown in Figure 1, for simulations involving 2^16 = 65536, 2^18 = 262144, and 2^20 = 1048576 particles. The vertical axis is the machine time required to perform a single cycle of the main integration loop, which decreases with the implemented number of processors. Optimally, this decrease should be linear. The horizontal axis is the number of processors implemented for each test. The uniform separation of the lines corresponds to the fact that the method scales with N*logN, where N is the particle number. The connected lines show how the calculation scales with processor number; scaling is quite linear out to 64 processors, and reasonably linear out to 256 processors. We find 256 processors to be optimum for our research calculations invoking 262,144 particles.
Figure 1
Our main research has involved simulations of colliding asteroids. Simulations using ESPH on the CRAY T3E, computed under this effort and rendered to video by Eric De Jong and Shigeru Suzuki of DIAL/JPL, have appeared on "CNN Headline News" and other television forums, and also in Sky and Telescope magazine and numerous newspapers. Figure 2 shows a time sequence from a calculation (t=0.1, 0.2, 0.3 seconds) in which an 8 m radius (house-sized) rock strikes the 1.6 km long Earth-crossing asteroid Castalia at 5 km/s, with an impact energy equal to 17 kilotons. Red is totally fractured rock, blue is intermediate fractured rock, and white particles represent the impactor, which is vaporized. Also available is an MPEG movie of the same event.
Figure 2
In the works is a much later time evolution of this collision, including the opening up of the crater bowl and the self-gravitational "dance" of the disrupted fragments. A naive estimate comparing ejection velocity (at this early time) with escape velocity (nominally 40 cm/s for Castalia) suggests that only ~10 percent of the ejecta escape from this collision. Only late time evolution will tell whether this result is in fact true and to what degree the re-aggregated structure resembles the original target.
The scientific motivation for this work is to better understand the accretion of small planets that grew, over time, into the large bodies of the Solar System, including Earth. The discovery of planetary systems around many other stars shows that this process is important in the universe at large. Accretion can at times be violent, as when asteroids slam into a planet—the event which killed the dinosaurs, for instance, or the event that formed the Moon very early on. After publishing our findings on mutual asteroid collisions in the journal Nature (Asphaug et al., June 4 1998), we discovered a great public interest in another aspect of our simulations: the possibility of disrupting, via nuclear explosions, or other means, a "hazard" asteroid that would otherwise collide with Earth and wipe out civilization.
Given the large number of small planetary bodies populating the heavens, including several observed at close range, and one (Eros) that will be the subject of intensive investigation beginning this February during the Near Earth Asteroid Rendezvous, we are satisfied to have developed the best tool available for studying the geophysical processes responsible for their shapes, sizes, and structures. Our research code ESPH has significant applications in other realms as well and will soon be employed to study phenomena such as the origin of the Moon, the formation of large impact craters on terrestrial planets, and the ejection of Earth-bound meteorites from the surface of Mars.
The code status is essentially complete for the CRAY T3E platform. We are tweaking the message passing aspects of our code to improve performance on large numbers (512 and greater) of processors. We have not yet turned on self-gravity in any calculation, although it is already incorporated into the tree structure. It slows down the computational time significantly and provides very little influence over the short-time evolution of small asteroids. We have also begun to explore the possibility of a particle-specific timestep within the code. This requires significant revision of the underlying integration scheme, although the payoff will be dramatic for very localized events such as hypervelocity impact.
The next major milestone for code development will be to develop a portable version of the code, probably via direct translation of Cray-specific (SHMEM) libraries to more universally adopted parallel structures such as MPI, HPVM, and Beowulf. Due to its unique topology, the CRAY T3E will remain our primary performance leader for the highest-resolution calculations. For other tasks such as the origin of the Moon, we hope to implement the code (with self-gravity) on low-cost arrays.
We have discovered that one needs to evolve asteroid collisions to much later time than previously considered, in order to derive the fraction of material escaping from a given event. For this reason we are focussing on long-term evolution of a smaller subset of runs than initially planned, rather than on short-term evolution of many runs. As greater amounts of processor time become available, we hope to commence with our second proposed effort, which is to model the impact ejection of meteorites from Mars. The physics of these impacts is quite similar, and should involve an extremely straightforward implementation of the current code.
Erik Asphaug
Department of Earth Sciences
University of California, Santa Cruz
asphaug@earthsci.ucsc.edu
831-459-2260
Kevin Olson
The University of Chicago
olson@sphere.uchicago.edu
Principal Investigator's Home Page:
http://www.es.ucsc.edu/~asphaug
Overview Article by Principal Investigator in Science:
http://www.sciencemag.org/cgi/content/full/278/5346/2070
CNN, ABC, NPR news reports involving interviews with Principal Investigator:
http://cnn.com/TECH/space/9806/03/asteroid.impact/index.html http://www.abcnews.com/sections/science/DailyNews/asteroid980603.html http://www.npr.org/ramfiles/980603.atc.14.ram