James Glimm and Xiaolin Li, State University of New York, Stony Brook

FronTier simulation of Rayleigh-Taylor instability with random initial perturbation: pH = 3, pL = 1, g = 0.14, p = 1, H = L = 1.667. Computational domain: 2 X 2 X 4, computational grid: 112 X 112 X 224, parallel partition: 8 X 8 X 1. The acceleration rate of the bubble envelope: = {hB/Agt2} = 0.075.

Research Objectives
We will conduct definitive simulations of two types of acceleration-driven fluid mixing: the steady acceleration-driven Rayleigh-Taylor (RT) instability, and the shock-driven Richtmyer-Meshkov (RM) instability. We will also study the impulsive acceleration (shock)-driven RM instability.

Computational Approach
We use the front tracking method to study the RT and RM instabilities. Recently we have implemented a robust grid-based method to handle the interface geometry. The traditional front tracking, known in contrast as grid-free tracking, also has advantages, in controlling the quality of the interface elements (triangles) and refined interface meshing. A hybrid combination of the two methods is best suited for study of both the RT and RM instabilities. The use of grid-free tracking at the initial stage of both problems gives an accurate startup of the problem. Grid-based tracking can handle the late-time chaotic stage of the fluid interface mixing without difficulty.

We have implemented front tracking in a software package known as FronTier. This code is portable to various parallel computational platforms. Another code, the TVD level set code, uses the untracked numerical scheme for the simulation of fluid interface instabilities. This code is easily vectorized and efficient. We use it as for scientific comparison with the FronTier code.

Accomplishments
The simulations in the past year study the Rayleigh-Taylor instability with randomly perturbed fluid interface. We have studied the growth rate under the variation of initial perturbation spectra, compressibility, and the growth rate in late-time chaotic mixing. In these studies, our numerical results are consistently closer to, or slightly larger than, the experimental value, in contrast to the results obtained by several other simulations. We believe that the difference is due to numerical diffusion in those simulations where fluid interface is not tracked. As a comparison, we also performed a simulation of the same problem using our own un-tracked TVD code. The comparison confirmed our conjecture.

Significance
Acceleration-driven fluid mixing instabilities play important roles in inertially confined nuclear fusion and in stockpile stewardship. Turbulent mixing is a difficult and centrally important issue for fluid dynamics, and impacts such questions as the rate of heat transfer by the Gulf Stream, resistance of pipes to fluid flow, combustion rates in automotive engines, and the late time evolution of a supernova. Our computational study will provide a better understanding of the development of these instabilities.

Publications
B. Cheng, J. Glimm, X. L. Li, and D. H. Sharp, "DNS simulations and subgrid models for fluid mixing," in Proc. 7th Int. Conf. on the Physics of Compressible Turbulent Mixing (St. Petersburg, 1999).

J. Glimm, J. Grove, X. L. Li, W. Oh, and D. Sharp, "A critical analysis of Rayleigh-Taylor growth rates," J. Comp. Phys. (submitted).

J. Glimm, J. Grove, X. L. Li, and D. C. Tan, "Robust computational algorithms for dynamic interface tracking in three dimensions," SIAM J. Sci. Comp. (submitted).

http://www.ams.sunysb.edu/~shock/FTdoc/FTmain.html