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Turbulent flows which also involve interactions with strong shocks and density variations arise in many diverse areas of science and technology. For example the explosive phenomena associated with supernova explosions, volcanic eruptions, accidental detonations involving natural gas leaks, shock wave lithotripsy to break up kidney stones, as well as the implosion of a cryogenic fuel capsule for inertial confinement fusion all involve dramatic compression and expansion of multiphase materials, their turbulent mixing and chemical reactions. Strong shock waves, strong acceleration and deceleration of heterogeneous materials and associated turbulent mixing play a critical part in these phenomena. Besides the multiscale hydrodynamic processes, these phenomena also involve other physics and chemistry rich in its complexity and nonlinearity, such as plasma physics, radiation transport, and complex chemical kinetics. The current ability to predict these flow phenomena is strongly limited by the models of turbulence used, and by the computational algorithms employed. This project, utilizing the petascale computational capabilities envisioned by the Department, provides an opportunity to revolutionize the scientific understanding of shockturbulence interactions and multimaterial mixing in complex flows by simulations at unparalleled fidelity. The project will consider turbulent flow configurations involving shockturbulence interaction and multimaterial mixing for fundamental scientific study, and for systematic model development, for example for use in largeeddy simulations in the context of applications to accelerated multimaterial flows. The team will also systematically evaluate different novel numerical approaches for nonlinear, multiscale shockturbulence interaction flow problems to establish the best practices and rigorous benchmarks in largeeddy simulations. Problems of shockturbulence interaction present a philosophical dilemma in numerical algorithm development. Methods designed to treat discontinuities and shocks are inherently dissipative for turbulence, and methods designed for turbulence (fluctuating fields with broadband variations) are ineffective for discontinuities. Capturing the interactions at unprecedented realism requires novel algorithms and effective use of software tools which allow the full benefit of the new algorithms to be realized on the massively parallel computer architectures. Flows involving the interaction of strong shocks with turbulence and density interfaces are central to laserdriven implosion of inertial confinement fusion plasmas, as well as in the broader Stockpile Stewardship mission of DOE. However, the current scientific understanding of shockturbulence interactions in complex configurations, and the ability to reliably predict these strongly nonlinear multiscale flows remains limited and imperfect. It is this area of science application, with relevance to inertial confinement fusion application and supernovae astrophysics, that the current Project aims to revolutionize by bringing together a team with deep expertise in numerical simulations of turbulence and turbulence physics, computational gas dynamics and shock wave physics, numerical analysis and nonlinear dynamics, and massively parallel computing. Science Application: Turbulence Project Title: Simulations of Turbulent Flows with Strong Shocks and Density Variations.
Principal Investigator: Sanjiva K. Lele Project Webpage: http://shocks.stanford.edu/
Participating Institutions and CoInvestigators: Funding Partners: U.S. Department of Energy  Office of Science, Advanced Scientific Computing Research, and the National Nuclear Security Agency. Budget and Duration: Approximately $0.8 million per year for five years ^{1} ^{1}Subject to acceptable progress review and the availability of appropriated funds

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