Objective: Rayleigh-Taylor instabilities result when a heavy fluid is supported by a less dense fluid against the force of gravity. Any perturbation along the interface between the two fluids will grow. The objective of this study is to determine how the growth rate of the instability and the rate of mixing between the two fluids depends on the numerical resolution of the calculation, or equivalently, on the effective viscosity of the two fluids.
Approach: The simulations were carried out using PROMETHEUS, a computer code that solves Euler's equations for compressible gas dynamics on a two-dimensional Cartesian grid using the Piecewise-Parabolic Method (PPM). The numerical resolution needed to reach the turbulent regime could only be obtained by running the code on a massively parallel computer.
Accomplishments: The code was modified to run on the 16,384-processor MasPar MP-2 and achieved a performance of 4 GFLOPS, which is approximately 2/3 the peak speed of the computer. The highest resolution calculation consumed 80 hours of CPU time and would have required nearly a month of CPU time on a single processor CRAY C90. These calculations are the highest resolution simulations ever performed of Rayleigh-Taylor instabilities and show for the first time the transition to turbulence in the flow. The calculations also show how the width of the mixing layer at a given time is reduced by the development of turbulence.
Significance: Understanding the rate of mixing caused by Rayleigh-Taylor instabilities is important to a wide variety of applications, including inertial confinement fusion, nuclear weapons explosions and stockpile management, and supernova explosions. Collaboration with scientists at Lawrence Livermore National Laboratory has begun to compare the results of these simulations with experiments being conducted on the Nova Laser to measure the amount of mixing due to Rayleigh-Taylor instabilities. If the results agree, it is hoped that future studies of mixing can rely more on the use of computer codes such as PROMETHEUS rather than experiments, which are more expensive and less flexible.
Status/Plans: Current calculations have been limited to two spatial dimensions in order to achieve maximum resolution. During the next couple of years, it is hoped that sufficiently powerful massively parallel computers will become available so that fully three-dimensional simulations can be carried out at comparable resolution.
MPEG Movie (6.3 Mbytes)
Point of Contact:
Bruce Fryxell
George Mason University
fryxell@neutrino.gsfc.nasa.gov
301-286-8567