Optimization in Fluid Mechanics

该项目旨在实现优化作为一种理论工具的全部潜力，以研究流体力学，因为我们需要更好地理解和控制我们周围的流动。例如，车辆在空气或水中行驶时所经历的阻力是能源的巨大消耗和碳排放的来源，这是英国迫切需要减少的。在过去，优化通常只用于简化的约束，如线性化的Navier-Stokes方程，以保持问题的可处理性。然而，最近的两项突破有力地表明，更复杂的优化问题的解决方案可以成功地计算出来，而最近的一项实验也突出了利用巧妙的几何设计可能实现的目标。该项目将寻求通过开发新的基于优化的方法来处理流体力学中的三个关键问题来利用这些令人兴奋的进展：1)如何系统地寻找新的非线性流动解来控制Navier-Stokes方程；2)如何通过边界几何来操纵非线性稳定性，从而设计出更节能的管道流体流动；3)如何计算完全湍流切变和对流流动中能量消耗（或阻力）的最佳严格上限估计。

This project aims to realise the full potential of optimisation as a theoretical tool to study fluid mechanics motivated by our need to better understand and control flows around us. As an exemplar, the drag experienced by vehicles as they move through either air or water is a huge consumer of energy and source of carbon emissions which the UK urgently needs to reduce. In the past, optimisation has generally only been used with simplified constraints such as the linearised Navier-Stokes equations to keep problems tractable. Recently, however, two breakthroughs now strongly suggest that the solutions to more sophisticated optimisation problems can be successfully computed and a recent experiment highlights what may be achieved using clever geometry design. This project will seek to exploit these exciting advances by developing new optimisation-based approaches to treat three key problems in fluid mechanics: 1) how to systematically search for new nonlinear flow solutions to the governing Navier-Stokes equations; 2) how to manipulate nonlinear stability via boundary geometry to design more energy-efficient fluid flows in pipelines; and 3) how to calculate the best rigorous upper estimates of energy consumption (or drag) in fully turbulent shear and convective flows.