Computer simulations of giant fluctuations in mixing fluids

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Thermal fluctuations in non-equilibrium systems exhibit remarkablebehavior compared to equilibrium systems. Giant fluctuations inbinary mixtures of miscible fluids have been observed, includingin recent experiments in microgravity. Novel mathematical andcomputational challenges need to be addressed in order to includethermal fluctuations in traditional computational fluid dynamics ina way that is consistent with statistical mechanics. This proposalis concerned with the design, mathematical analysis, and computerimplementation of finite-volume methods for fluctuating hydrodynamicsof fluid mixtures, as well as applications to diffusively mixingfluids in gravity. The following research directions are proposed:(1) Multi-resolution numerical schemes for solving the compressiblestochastic continuum equations; (2) Algorithms for incompressible,and (3) low Mach fluctuating hydrodynamics of miscible mixtures onstaggered and collocated grids; (4) Simulations of giant fluctuationsand comparisons to experiments; (5) Study of the contributionof advection by velocity fluctuations to transport in finitenon-equilibrium systems.Flows at micro and nano scales typical of new devices and biologicalsystems are affected by thermal fluctuations. These effects are oftenassumed small and are not included in traditional computationalfluid dynamics. However, giant fluctuations in the concentrationof a polymer solution have been observed in recent experimentsconducted in microgravity on a research space shuttle. Computersimulations are ideally suited for studying the details of thisphenomenon and comparing the predictions of existing theory tothe experimental findings. However, our community still lacksthe appropriate computational tools, including both algorithms andlarge-scale parallel codes, to attack this problem. The investigatorand his colleagues will develop such tools and use them to answerimportant scientific questions concerning fluctuations in fluids, inclose collaboration with experimentalists. The developed algorithmswill be implemented in a public domain code whose development is fundedthrough a Software Infrastructure for Sustained Innovation NSF grant.