Multi-fidelity optimization methods promise a high-fidelity optimum at a cost only slightly greater than a low-fidelity optimization. This promise is seldom achieved in practice, due to the requirement that low- and high-fidelity models correlate well. In this article, we propose an efficient bi-fidelity shape optimization method for turbulent fluid-flow applications with Large-Eddy Simulation (LES) and Reynolds-averaged Navier-Stokes (RANS) as the high- and low-fidelity models within a hierarchical-Kriging surrogate modelling framework. Since the LES–RANS correlation is often poor, we use the full LES flow-field at a single point in the design space to derive a custom-tailored RANS closure model that reproduces the LES at that point. This is achieved with machine-learning techniques, specifically sparse regression to obtain high corrections of the turbulence anisotropy tensor and the production of turbulence kinetic energy as functions of the RANS mean-flow. The LES–RANS correlation is dramatically improved throughout the design-space. We demonstrate the effectivity and efficiency of our method in a proof-of-concept shape optimization of the well-known periodic-hill case. Standard RANS models perform poorly in this case, whereas our method converges to the LES-optimum with only two LES samples.

多保真度优化方法保证了高保真度优化，而成本仅比低保真度优化稍高。由于要求低保真模型和高保真模型具有良好的相关性，因此在实践中很少实现这一承诺。在本文中，我们提出了一种有效的双保真形状优化方法，该方法将湍流应用与大涡模拟（LES）和雷诺平均Navier-Stokes（RANS）作为分层中的高保真和低保真模型一起使用-克里格代理模型框架。由于LES-RANS相关性通常很差，因此我们在设计空间中的单个点使用完整的LES流场，以得出定制的RANS闭合模型在那个时候重现LES。这是通过机器学习技术实现的，特别是稀疏回归以获得湍流各向异性张量和湍流动能的产生作为RANS平均流函数的高度校正。在整个设计空间中，LES-RANS相关性得到了显着改善。我们在著名的周期山案例的概念验证形状优化中证明了我们方法的有效性和效率。在这种情况下，标准RANS模型的性能较差，而我们的方法仅用两个LES样本收敛到LES最优。