NERSC 1999 Annual Report

We will conduct definitive simulations of acceleration-driven fluid mixing, including the steady acceleration driven Rayleigh-Taylor instability and the shock driven Richtmyer-Meshkov instability.

A Rayleigh-Taylor unstable mixing layer results from steady acceleration applied to a randomly perturbed initial interface separating fluids of distinct densities, with the light fluid pushing the heavy fluid. The reported experimental value for the effective acceleration rate, , ranges from 0.04 to 0.077. Most simulation studies give lower values for , ranging from 0.015 to 0.03. Our simulation of this problem has achieved an acceleration rate between 0.075 and 0.08, which is probably somewhat high, but is consistent with reported experimental values. In view of this success, we propose to explore the dependence of on numerical parameters such as mesh refinement, enlargement of the statistical ensemble, longer running time and compressibility, to obtain a definitive value of . We also propose to determine the specific numerical issues responsible for the spread of the reported simulation values of .

The shock-driven Richtmyer-Meshkov instability develops more slowly, and for this reason, the solution is more strongly dependent on initial parameters which are poorly understood. Our simulation study will explore these physical parameters.

Computational Approach


	The interface between heavy and light fluids is displayed in a late time simulation of the acceleration driven Rayleigh-Taylor instability. The simulation has undergone more than one generation of bubble merger.

We used the front tracking method to study RT and RM instabilities. Front tracking features high resolution of physical quantities at the material interface, thus giving a more accurate solution to the physical problem. Both grid-based and grid-free tracking methods are used at different stages of the simulation. We have implemented the front tracking method in a software package known as the FronTier. This code is written in C and is portable to various parallel computational platforms including the Cray T3E. FronTier has recently been extended to 3D and is ready for production usage.

Accomplishments

A primary accomplishment was a simulation of the RT random surface instability in 3D which is consistent with experimental values for the growth rate of the bubble interface. We also extended FronTier to handle simulations in cylindrical (r, 0) geometry, which will enable 2D spherical simulations in the future. We are currently simulating a variety of random surface and single mode RM instability problems, to determine the dependence of the solution on the problem parameters. We are simulating the instability and breakup of a jet in 3D. Earlier studies showed control of mesh orientation for 2D implosion and agreement with Nova laser data for strong shock RM instability.

Significance

Acceleration-driven fluid mixing instabilities play important roles in inertially confined nuclear fusion and stockpile stewardship reseasrch. 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 Proceedings of the 7th International Conference on the Physics of Compressible Turbulent Mixing, St. Petersberg (1999).

J. Glimm, M. J. Graham, J. Grove, X. L. Li, T. M. Smith, D. Tan, F. Tangerman, and Q. Zhang, "Front tracking in two and three dimensions," J. Comp. Math. 7, 1 (1998).

J. Glimm, D. Saltz, and D. H. Sharp, "Statistical evolution of chaotic fluid mixing," Phys. Rev. Lett. 80, 712 (1998).

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


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