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以及相应的高性能计算（HPC）资源的增加，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，仍然存在各种多尺度，物理复杂的流动，仍然知之甚少，并已被证明是非常具有挑战性的预测计算方法。这种流动将包括但不限于：（i）在先进的航空航天推进系统中遇到的湍流、反应和多相流动;（ii）气体和导电流体和等离子体的高速流动;以及（iii）微尺度和/或稀薄非平衡流动。为了能够以预测的方式更常规地求解这种流动，需要在数值方法和CFD算法设计方面取得进一步的和相当显著的进展，沿着改进相关物理过程的数学模型。对于后者，数学模型，提供显着降低的复杂性，同时保持解决方案的保真度将是非常可取的。因此，拟议的研究将集中在开发和应用的新的，准确的，高效的，和强大的自适应解决方案的方法和模型，用于描述多尺度的物理复杂的流使用HPC架构。这项研究的主要内容将包括：（一）利用多块贴体网格和混合网格，为复杂几何形状和界面开发基于输出的各向异性自适应网格加密技术;（二）加强高阶有限体积和相关通量重构空间离散化方法，并辅之以高阶时间离散化方案，以提高解的精度; ㈢根据各种传输现象的矩封闭法，开发和有效解决改进的数学模型，包括非平衡气体和等离子体流动、多相雾化和喷雾形成、纳米级固体烟灰微粒的形成、氧化和传输，以及参与介质中的辐射传热;以及（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，用于评估和改进物理模型以及改进模拟预测。将通过应用于反应和多相流、非平衡气流以及高速空间等离子体流的预测来评估所提出的用于多尺度、物理复杂问题的计算工具的潜力、能力和性能。后者将包括模拟空间气象现象。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，从而能够模拟更广泛的流动。

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.