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通过用于流动分析的定常雷诺平均Navier-Stokes(RANS)方程来处理的，并使用伴随灵敏度方法来获得诸如升力物体的阻力等流动参数相对于设计参数的梯度。然而，当耦合到非定常的、尺度分辨的湍流模拟时，当前的伴随方法是无效的。这从根本上是由于湍流的混沌性质及其对扰动的高度敏感性。在实践中，伴随方程产生指数级增长的解，导致非物理梯度，不能反映设计更改的真实影响。随着当前工程设计的趋势，非定常湍流模拟将逐渐取代RAN用于流动分析和设计，需要更好的伴随设计和优化方法。

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.