Computer simulations of giant fluctuations in mixing fluids

与平衡系统相比，非平衡系统中的热涨落表现出显著的行为。在混合流体的二元混合物中观察到了巨大的波动，包括在最近的微重力实验中。需要解决新的数学和计算挑战，以便以与统计力学一致的方式在传统计算流体力学中包含热涨落。本文涉及流体混合物波动流体力学的有限体积法的设计、数学分析和计算机实现，以及在重力条件下扩散混合流体的应用。提出了以下研究方向：(1)求解可压缩弹塑性连续介质方程的多分辨率数值格式；(2)不可压缩的算法；(3)交错和配置网格上可混溶混合物的低马赫脉动流体动力学；(4)巨大脉动的模拟和与实验的比较；(5)有限非平衡系统中速度涨落对输运的贡献的研究。这些影响通常被认为是小的，并且不包括在传统的计算流体力学中。然而，最近在研究航天飞机上进行的微重力实验中，观察到了聚合物溶液浓度的巨大波动。计算机模拟非常适合于研究这一现象的细节，并将现有理论的预测与实验结果进行比较。然而，我们的社区仍然缺乏适当的计算工具，包括算法和大规模并行代码，来解决这个问题。这位研究人员和他的同事们将开发这样的工具，并与实验者密切合作，用它们来回答有关流体波动的重要科学问题。开发的算法将在公共领域代码中实现，该代码的开发由NSF持续创新软件基础设施拨款资助。

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.