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

将开发一个新的框架，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边界附近发生的过程的简单描述，比如对均匀状态的线性化干扰，要么依赖于一系列试图减轻域截断的虚假工件的技术。目前的工作是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流模拟中使用的亚网格尺度模型。该公式明确地认识到，在一般系统（尤其是非齐次和非线性PDE）中，域截断和过滤一样，是一个建模问题——结果是无法从第一原理中恢复的“丢失信息”。许多现有的技术（尤其是阻尼层）隐含地提供了这样一个模型，但我们的假设，在可压缩流和声学应用的初步计算的支持下，是更好的模型可以通过利用与亚网格尺度建模技术的强烈类比来开发。这个类比是基于滤波和加窗在实空间和傅里叶空间中所起的双重作用。该提案详细介绍了一个合理排序的研究计划，包括检查几种不同的超网格模型（基于对现有子网格模型的类比），详细的计算和与先前在不可压缩和可压缩流动，声学和电磁领域的方法的比较，以及模型和离散系统的稳定性和收敛性的详细分析。人们常说，模拟正在成为科学的“第三条腿”，在理论和实验之外占据重要地位。在工程中，模拟是一种重要的工具，它使设计和优化基于第一性原理，而不是经验关联。然而，只有当底层系统被正确建模时，计算才有用。事实上，流体动力学、声学和电磁波中的许多相关系统无法用现有技术可靠地模拟。特别是人工域截断技术，在这些领域和相关领域的许多应用中都是一个前沿项目。人工域截断（或人工边界条件）是指为了减少计算工作量而只希望模拟较大系统的一部分的情况。目前的研究将提供新一代的此类技术，这些技术基于一个严格且经过充分验证的建模框架，即超级电网规模模型。该研究的成功结果可能对科学和工程设计导向的模拟产生深远的影响。

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.