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

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.