Abstract A wide range of previously designed methods for faster parametrization of partial differential equations requires them to be solved using existing finite volume, finite element, and finite difference solvers. Due to the requirement of high degrees of freedom to accurately model the physical system, computational costs often becomes a bottle-neck. It poses challenges to conducting efficient repeated parametric sampling of the input parameter that disrupts the whole design process. Model reduction techniques adopted to high fidelity systems provide a basis to accurately represent a physical system with a lower degree of freedom. The present work focuses on one such method for high-fidelity simulations that combines finite volume strategy with proper orthogonal decomposition and Galerkin projection to test reduced-order models for high Reynolds number flow applications. The model is first benchmarked against flow around a cylinder for which extensive numerical and experimental data is available in the literature. The models are then tested to full-scale NREL 5MW offshore wind turbines to evaluate wake evolution in the downstream direction. The simulations results show relative errors of wind turbines for the first seventy modes approach 4.7% in L2-norm for velocities.

中文翻译：

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适当正交分解的海上风机尾流降阶模型

摘要 先前为加快偏微分方程参数化而设计的各种方法需要使用现有的有限体积、有限元和有限差分求解器来求解。由于对物理系统的精确建模需要高自由度，计算成本往往成为瓶颈。它对中断整个设计过程的输入参数进行有效的重复参数采样带来了挑战。用于高保真系统的模型缩减技术为准确表示具有较低自由度的物理系统提供了基础。目前的工作重点是一种用于高保真模拟的方法，该方法将有限体积策略与适当的正交分解和伽辽金投影相结合，以测试高雷诺数流应用的降阶模型。该模型首先针对圆柱体周围的流动进行基准测试，文献中提供了大量的数值和实验数据。然后将模型在全尺寸 NREL 5MW 海上风力涡轮机上进行测试，以评估下游方向的尾流演变。仿真结果表明，在速度的 L2 范数中，前 70 种模式的风力涡轮机的相对误差接近 4.7%。然后将模型在全尺寸 NREL 5MW 海上风力涡轮机上进行测试，以评估下游方向的尾流演变。仿真结果表明，在速度的 L2 范数中，前 70 种模式的风力涡轮机的相对误差接近 4.7%。然后将模型在全尺寸 NREL 5MW 海上风力涡轮机上进行测试，以评估下游方向的尾流演变。仿真结果表明，在速度的 L2 范数中，前 70 种模式的风力涡轮机的相对误差接近 4.7%。