Adaptively Tuned High-Order Unstructured Finite-Volume Methods for Turbulent Flows

湍流流体流动的特征是流体颗粒的看似无序和不可预测的运动，这些运动开始旋转并产生漩涡。一些过程和产品，如风力涡轮机、燃烧、汽车、飞机，注定要与湍流共存。因此，了解湍流对于提高许多工艺和产品的性能至关重要。在描述流体流动的Navier-Stokes方程的全部秘密被解开之前，跨多个学科的研究人员将继续依靠实验和计算流体动力学（CFD）来研究湍流。大多数对科学家和工程师具有实际重要性的湍流具有高雷诺数的特征，具有广泛的空间和时间尺度。使用Navier-Stokes方程的直接数值模拟（DNS）来解决所有尺度所需要的分辨率由于计算成本是不可行的，即使使用当今最强大的超级计算机。大涡模拟（LES）系列方法已经成为瞬态模拟的一种优雅的替代方法，在瞬态模拟中，大尺度被解决，而未解决的小尺度的影响被建模。非线性数值方法被广泛用于可压缩LES模拟，因为它们可以表现出两个重要的性质。首先，在流动不连续区域具有非振荡特性；其次，在流动的光滑区域具有低数值耗散。大量的研究工作致力于在这两种特性之间取得完美的平衡。然而，它们的调谐仅限于控制均匀笛卡尔网格上的数值耗散和色散，因为没有成熟的技术将它们的调谐扩展到由不同元素类型组成的网格上。本研究旨在开发一种新的非线性方法，通过引入适用于任何类型的非结构化网格的合适的新指标，可以提供自动耗散和色散调整（ADDA）。这些方法将应用于一系列精心选择的湍流问题，包括使用非结构化网格的中等和高雷诺数，并使用国家ARCHER2高性能计算（HPC）设施。开发的方法将在免费的开源ucns3d CFD软件中提供，并将由生成的数据集支持，这些数据集将在开放存储库中提供。最后，根据最新的英国流体网络2021年9月报告，这项研究将对英国流体动力学行业产生相当大的影响，该行业从2200多家公司产生价值139亿英镑的产出，雇佣45000人，而英国从事流体动力学的公司总营业额超过2000亿英镑，雇佣超过50万人。这项研究将为英国主导的研究做出贡献，使CFD软件的开发能够在所有行业中常规使用，并使英国成为CFD领域的世界领导者，从而推动全球公司与英国专家合作，推动创新，提高生活质量。

Turbulent fluid flow is characterised by the seemingly disordered and unpredictable movement of fluid particles that begin to swirl and create eddies. Several processes and products such as wind-turbines, combustion, cars, aircrafts are fated to coexist with turbulence. Therefore, understanding turbulent flows, is of paramount importance to improve the performance of many processes and products. Until the full secrets of the Navier-Stokes equations that describe fluid flows are unlocked, researchers across several disciplines will continue to rely on experiments and computational fluid dynamics (CFD) for casting new light on turbulent flows.Most turbulent flows of practical importance to scientists and engineers are characterised by high-Reynolds numbers, with a wide range of spatial and temporal scales available. The resolution required to resolve all the scales present using direct numerical simulation (DNS) of the Navier-Stokes equations is not feasible due to the computational cost, even with the most powerful supercomputers available today. Large eddy simulation (LES) family of methods have established themselves as an elegant alternative for transient simulations, where the large scales are resolved, and the effects of the unresolved small scales is modelled. Non-linear numerical methods are widely used for compressible LES simulations since they can exhibit two important properties. Firstly, a non-oscillatory behaviour across flow discontinuities and secondly a low-numerical dissipation in smooth regions of the flow. A considerable body of research work has been devoted in striking the perfect balance between these two properties. However, their tuning has been limited to controlling the numerical dissipation and dispersion on uniform Cartesian meshes, since there are no established techniques to expand their tuning to meshes consisting of different element types.This research seeks to develop a new class of non-linear methods, that can offer automatic dissipation and dispersion adjustment (ADDA), through the introduction of suitable novel metrics, that are applicable to any type of unstructured mesh. These methods will be applied to a series of carefully selected turbulent flow problems including moderate and high Reynolds numbers using unstructured meshes, and using the national ARCHER2 High Performance Computing (HPC) facility. The developed methods will be available in the free open source ucns3d CFD software and will be supported by the generated datasets that will be available in a open repositories.Finally this research will make a considerable impact on the UK fluid dynamics industry that generates £13.9 billion worth of output from over 2,200 firms and employs 45,000 people, while the total UK turnover of firms engaged in fluid dynamics exceeds £200 billion and employ over half a million people according to the latest UK Fluids Network Sept 2021 report. This research will contribute towards UK-led research that enables the development of CFD software that is routinely employed in all industry sectors and has established the UK as a world leader in CFD that in turn drives global companies to engage with UK experts for driving innovation for improving the quality of life.