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看起来无序和不可预测的运动，开始旋转并产生漩涡。几个过程和产品，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是至关重要的。在描述流体流动的Navier-Stokes方程的全部秘密被解开之前，几个学科的研究人员将继续依靠实验和计算流体力学(CFD)来为湍流提供新的线索。对于科学家和工程师来说，大多数具有实际意义的湍流具有高雷诺数的特征，具有广泛的空间和时间尺度。由于计算成本的原因，即使使用当今最强大的超级计算机，使用Navier-Stokes方程的直接数值模拟(DNS)来解析所有存在的尺度所需的分辨率也是不可行的。大涡模拟(LES)方法是解决大尺度问题、模拟小尺度问题的一种有效的方法。非线性数值方法因其具有两个重要性质而被广泛应用于可压缩大涡模拟。第一，流动不连续区域的非振荡行为，第二，流动光滑区域的低数值耗散。为了在这两个性质之间取得完美的平衡，人们进行了大量的研究工作。然而，它们的调谐一直局限于控制均匀笛卡尔网格上的数值耗散和色散，因为还没有成熟的技术将它们的调谐扩展到由不同单元类型组成的网格上。本研究试图通过引入适用于任何类型非结构网格的合适的新度量来开发一类新的非线性方法，该方法可以提供自动耗散和色散调整(ADDA)。这些方法将被应用于一系列精心选择的湍流问题，包括使用非结构网格和国家ARCHER2高性能计算(HPC)设施的中等和高雷诺数。开发的方法将在免费开源ucns3d CFD软件中使用，并将得到开放资源库中可用的生成数据集的支持。最终，这项研究将对英国流体动力学行业产生重大影响，该行业从2200多家公司产生139亿GB的产出，雇佣了4.5万名员工，而根据最新的英国流体网络2021年9月报告，从事流体动力学的公司在英国的总营业额超过2000亿GB，雇佣了超过50万人。这项研究将有助于英国主导的研究，使CFD软件的开发成为所有行业的常规应用，并使英国成为CFD领域的世界领先者，进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.