New Optimisation Methods for Scale-Resolving Turbulent Flow Simulation

在流体力学中，形状设计问题传统上是用定常的雷诺平均纳维尔-斯托克斯（RANS）方程来进行流动分析，并使用伴随灵敏度方法来获得流量（如升力体阻力）相对于设计参数的梯度。然而，目前的伴随方法是无效的，当耦合到非定常，尺度分辨湍流模拟。这主要是由于湍流的混沌特性及其对扰动的高度敏感性。在实践中，伴随方程产生指数增长的解决方案，导致不反映设计变化的真实影响的非物理梯度。随着当前工程设计的趋势，非定常湍流模拟将逐渐取代RANS用于流动分析和设计，需要更好的设计和优化伴随方法。

In fluid mechanics, shape design problems have been traditionally tackled with steady Reynolds-Averaged-Navier-Stokes (RANS) equations for flow analysis and using adjoint sensitivity methods to obtain the gradient of flow quantities, such as the drag of an lifting body, with respect to design parameters. Current adjoint methods, however, are ineffective when coupled to unsteady, scale-resolving turbulent flow simulations. This is fundamentally due to the chaotic nature of turbulence and its high sensitivity to perturbations. In practice, the adjoint equation produces exponentially growing solutions, leading to unphysical gradients that do not reflect the true influence of design changes. With current trends in engineering design, where unsteady turbulent flow simulation will gradually replace RANS for flow analysis and design, better adjoint methods for design and optimisation are needed.