Development of a super-grid-scale model for artificial boundaries in fluid dynamics and other wave pheonmena

将开发一种新的框架，用于模拟各种应用中的人工边界条件，包括流体动力学、声学和电磁波传播。以前的方法要么依赖于对发生在边界附近的那些过程的简单描述，例如将扰动线性化到均匀状态，要么依赖于一系列试图减少区域截断的虚假伪影的自适应技术。本工作基于超网格尺度模型的概念，该模型在许多方面类似于湍流大涡模拟中使用的亚网格尺度模型。该公式明确认识到，在一般系统(特别是非齐次和非线性偏微分方程组)中，域截断与滤波一样，是一个建模问题--其结果是无法从第一原理恢复的“信息丢失”。许多现有的技术(特别是阻尼层)隐含地提供了这样的模型，但我们的假设得到了可压缩流动和声学应用的初步计算的支持，即可以通过利用与亚网格尺度模拟技术的强烈相似来开发更好的模型。这种类比是基于滤波和加窗在实空间和傅立叶空间中所扮演的双重角色。该提案详细介绍了合理排序的研究计划，包括检查几种不同的超网格模型(基于对现有亚网格模型的类比)，在不可压缩和可压缩流动、声学和电磁领域的详细计算和与以前方法的比较，以及对模型和离散系统的稳定性和收敛的详细分析。人们常说，模拟正在成为科学的第三条腿，在理论和实验之外发挥着重要的作用。在工程中，模拟是一种重要的工具，它使设计和优化能够基于第一原理而不是经验相关性。然而，只有当底层系统建模正确时，计算才是有用的。事实上，许多流体动力学、声学和电磁波的相关系统不能用现有的技术进行可靠的模拟。尤其是人工区域截断技术在这些领域和相关领域的许多应用中是一个重要的项目。人工区域截断(或人工边界条件)指的是为了减少计算工作量而希望只模拟较大系统的一部分的情况。本研究将提供新一代这样的技术，它们基于一种被称为超网格尺度模型的严格且经过充分验证的建模框架。拟议研究的成功结果可能会对面向科学和工程设计的远范围影响模拟产生影响。

A new framework for modeling artificial boundary conditions in a variety ofapplications, including fluid dynamics, acoustics, and electromagnetic wavepropagation, will be developed. Previous approaches have relied either onsimple descriptions of those processes occurring near boundaries, such aslinearized disturbances to uniform states, or on a range of ad hoctechniques that attempt to mitigate spurious artifacts of domain truncation.The present work is based on the concept of a super-grid-scale model that isin many ways analogous to sub-grid-scale models that are used in Large EddySimulations of turbulent flows. The formulation explicitly recognizes thatin general systems (especially inhomogeneous and nonlinear PDE), domaintruncation, like filtering, is a modeling problem--the result is ``missinginformation'' that cannot be recovered from first principles. Many existingtechniques (especially damping layers) implicitly supply such a model, butour hypothesis, backed by preliminary calculations in compressible flow andacoustic applications, is that better models can be developed by exploitinga strong analogy with sub-grid-scale modeling techniques. The analogy isbased on the dual roles that filtering and windowing play in real andFourier space. The proposal details a rationally sequenced research programthat includes examination of several different super-grid models (based onanalogies to existing sub-grid models), detailed computations and comparisonwith previous methods in the areas of incompressible and compressible flow,acoustics, and electromagnetic, and detailed analysis of stability andconvergence of the models and discretized systems.It is often said that simulation is becoming the 'third leg' of science,taking an important place beside theory and experiment. In engineering,simulation is an essential tool that enables design and optimization basedon first-principles rather than empirical correlations. However,computation is only useful when the underlying system is correctly modeled.Indeed, many relevant systems in fluid dynamics, acoustics, andelectromagnetic waves cannot be reliably simulated with existing techniques.Techniques for artificial domain truncation, in particular, are a pacingitem in many applications in these and related fields. Artificial domaintruncation (or artificial boundary conditions) refers to situations whereone wishes to simulate only a portion of a larger system in order to reducecomputational effort. The present research will provide a new generation ofsuch techniques that are based on a rigorous and well-validated modelingframework called the super-grid-scale model. Successful outcome of theproposed research has potential for far-ranging impact scientific andengineering design-oriented simulations.