Enabling Long-Time Accuracy in Turbulent Flow Simulations

该奖项是根据2009年美国复苏和再投资法案（公法111-5）资助的。首席研究员（PI）建议研究数学模型和数值方法，以实现湍流流动模拟的长期准确性。第一个方面是通过数学和数值分析，发展高精度近似反褶积正则化模型和相关算法。对这些模型及其方法的分析将导致i）开发具有更高精度和更有效算法的更好模型，以及ii）离散化策略和稳定化技术，这将在更长的时间间隔内提高稳定性和精度。第二个方面是发展一种基于增强物理的方案，用于计算一般区域上的三维不可压缩Navier-Stokes方程的解。除了质量、动量和能量外，通过保存螺旋度，将通过该方案提供的额外物理保真度来实现长期精度。为了确认预期，将对各种域和边界条件进行大规模长时间模拟。基于增强物理的方案将扩展到近似反卷积模型，这是一种罕见的模型，以其连续形式保存能量和螺旋度。此外，我们亦会探讨如何将基于增强物理的方案扩展为浅水方程的能量和位涡拟能守恒方案，从而得到更精确、更有物理意义的三维湍流近似计算，从而使计算解的精度能够长期保持。对于&飞机、汽车和输送流体的设备（包括医疗设备）的设计来说，精确模拟湍流流动的需求是至关重要的&。由于需要模拟的流动（例如多相的，例如在核反应堆中），基本困难与湍流相同，因此单相湍流的进展是直接相关的。 长时间间隔的准确性，以及基于物理的模型/离散化提供的可移植性，将大大减少对昂贵的实验数据的需求，并大大加快设计过程。

This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5).The principal investigator (PI) proposes to research mathematical models and numerical methods for enabling long time accuracy in turbulent fluid flow simulations. The first aspect is the development, through mathematical and numerical analysis, of high accuracy approximate deconvolution regularization models and related algorithms. Analysis of these models and their methods will lead to i) the development of better models with increased accuracy and more efficient algorithms, and ii) discretization strategies and stabilization techniques that will improve stability and accuracy over longer time intervals. The second aspect is the development of an enhanced-physics based scheme for computing solutions to the 3d incompressible Navier-Stokes equations on general domains. By conserving helicity in addition to mass, momentum and energy, long-time accuracy will be achieved through the additional physical fidelity offered by the scheme. To confirm expectations, large-scale long time simulations will be performed on a variety of domains and boundary conditions. The enhanced physics based scheme will be extended to approximate deconvolution models, which are a rare breed of models that conserve energy and helicity in their continuous forms. Additionally, extension of the enhanced-physics based scheme to an energy and potential enstrophy conserving scheme for the shallow water equations will be explored.The proposed research will lead to more accurate, more physically meaningful, computable approximations to 3d turbulent flow, which in turn will enable long-time accuracy of computed solutions. The need to accurately simulate turbulent fluid flow is paramount for the design of planes, cars, and devices (including medical) that transport fluids.Even for designs where more complex flows need simulated (e.g.multiphase such as in nuclear reactors), the fundamental difficulty is the same as for turbulent flow, and so progress in single phase turbulence is directly relevant. Accuracy over long-time intervals, as well as the portability offered by physics-based models/discretizations, will greatly reduce the need for expensive experimental data and substantially accelerate the design process.