Accurate, Efficient, and Robust Adaptive Solution Methods and Models for Predicting Multi-Scale Physically-Complex Flows

随着近15-20年来数值方法的显著改进和高性能计算（HPC）资源的相应增加，计算流体动力学（CFD）已成为科学和工程领域的重要使能技术。然而，尽管取得了这些进展，仍然存在各种各样的多尺度、物理复杂的流动，人们对这些流动的理解仍然很差，而且通过计算方法预测这些流动非常具有挑战性。这些流动包括但不限于：(1)在先进的航空推进系统中遇到的湍流、反应性和多相流；（ii）气体、导电流体和等离子体的高速流动；（iii）微观和/或稀薄的非平衡流动。为了能够以预测的方式对此类流动进行更常规的求解，需要在数值方法和CFD算法设计方面取得进一步的重大进展，并改进相关物理过程的数学模型。对于后者，在保持解决方案保真度的同时显著降低复杂性的数学模型将是非常理想的。因此，建议的研究将侧重于开发和应用新颖、准确、高效和强大的自适应解决方案方法和模型，用于使用高性能计算架构描述多尺度物理复杂的流。研究的关键要素将包括：(i)开发基于输出的各向异性自适应网格细化（AMR）技术，用于使用多块体装配和混合网格的复杂几何形状和界面；（ii）将高阶有限体积和相关通量重建空间离散化方法与互补的高阶时间离散化方案相结合，以提高求解精度；（iii）基于矩闭的各种输运现象的改进数学模型的开发和有效解决，包括非平衡气体和等离子体流动，多相雾化和喷雾形成，纳米级固体烟尘颗粒的形成，氧化和传输，以及参与介质中的辐射传热；（iv）开发和利用参数估计、数据驱动和可能的数据同化技术的组合，以评估和改进物理模型和改进模拟预测。提出的计算工具的潜力、能力和性能将通过应用于预测反应性和多相流动、非平衡气体流动以及高速空间等离子体流动来评估多尺度、物理复杂问题。后者将包括空间天气现象的模拟。与现有方法相比，拟议的研究预计将导致计算效率提高一个数量级以上，从而能够模拟更大范围的流动。

With the significant improvements in numerical methods over the last 15-20 years and correspondoing increases high-performance computing (HPC) resources, computational fluid dynamics (CFD) has become an important enabling technology in science and engineering. However, despite these advances, there remain a variety of multi-scale, physically-complex flows that are still poorly understood and have proven to be very challenging to predict by computational methods. Such flows would include but are not limited to: (i) turbulent, reactive, and multi-phase flows encountered in advanced aerospace propulsion systems; (ii) high-speed flows of gases and conducting fluids and plasmas; and (iii) micro-scale and/or rarefied non-equilibrium flows. In order to enable the more routine solution of such flows in a predictive manner, further and rather significant advances in numerical methods and CFD algorithm design are required, along with improved mathematical models for the relevant physical processes. For the latter, mathematical models that offer significant reductions in the complexity while retaining solution fidelity would be extremely desirable. The proposed research will therefore focus on the development and application of novel, accurate, efficient, and robust adaptive solution methods and models for describing multi-scale physically-complex flows using HPC architectures. Key elements of the research will include: (i) the development of output-based anisotropic adaptive mesh refinement (AMR) techniques for complex geometries and interfaces using multi-block body-fitted and hybrid grids; (ii) the enhancement of high-order finite-volume and related flux-reconstruction spatial discretization methods coupled with complementary high-order temporal discretization schemes for improved solution accuracy; (iii) the development and efficient solution of improved mathematical models based on moment closures for various transport phenomena, including non-equilibrium gaseous and plasma flows, multi-phase atomization and spray formation, the formation, oxidation, and transport of nanoscale solid soot particulates, and radiative heat transfer in participating media; and (iv) the development and exploitation of a combination of parameter estimation, data-driven, and possibly data-assimilation techniques for both assessing and improving physical models and improving simulation predictions. The potential, capabilities, and performance of the proposed computational tools for multi-scale, physically-complex problems will be assessed through application to the prediction of reactive and multi-phase flows, non-equilibrium gaseous flows, as well as high-speed space plasma flows. The latter would include the simulation of space weather phenomena. The proposed research is expected to result in a more that one order of magnitude improvement in computational efficiency compared to existing methods, thereby enabling the simulation of a far wider range of flows.