Simulating forced time-periodic flows in industrial applications presents significant computational challenges, partly due to the need to overcome costly transients before achieving time-periodicity. Reduced-order modelling emerges as a promising method to speed-up computations. We extend upon the work of Lotz et al. (2024) where a time-periodic space–time model is introduced. We present a time-periodic reduced-order model that directly finds the time-periodic solution without requiring extensive time integration. The reduced-order model gives a reduction in variables in both space and time. Our approach involves a POD-Galerkin reduced-order model based on a time-periodic full-order model that employs isogeometric analysis, residual-based variational multiscale turbulence modelling and weak boundary conditions. The projection-based reduced-order model inherits these features. We evaluate the reduced-order model with numerical experiments on moving hydrofoils. The motion is known a priori and we restrict ourselves to two spatial dimensions. In these experiments we vary the Strouhal and Reynolds numbers, and the motion profile respectively. Reduced-order model solutions agree well with those of the full-order model. The errors over the entire time period of thrust and lift forces are less than 0.2%. This includes complex scenarios such as the transition from drag to thrust production with increasing Strouhal number. Our time-periodic reduced-order model offers speed-ups ranging from to compared to the full-order model, depending upon the basis size. This makes it an appealing solution for prescribed time-periodic problems, with potential for additional speedup through nonlinear reduction techniques such as hyper-reduction.

中文翻译：

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基于投影的时间周期问题降阶建模，并应用于流过扑动水翼的情况


在工业应用中模拟强制时间周期流提出了巨大的计算挑战，部分原因是在实现时间周期之前需要克服代价高昂的瞬态。降阶建模成为一种有前途的加速计算的方法。我们扩展了 Lotz 等人的工作。 （2024）其中引入了时间周期时空模型。我们提出了一种时间周期降阶模型，可以直接找到时间周期解，而不需要大量的时间积分。降阶模型减少了空间和时间上的变量。我们的方法涉及基于时间周期全阶模型的 POD-Galerkin 降阶模型，该模型采用等几何分析、基于残差的变分多尺度湍流建模和弱边界条件。基于投影的降阶模型继承了这些特征。我们通过移动水翼的数值实验来评估降阶模型。该运动是先验已知的，我们将自己限制在两个空间维度上。在这些实验中，我们分别改变斯特劳哈尔数和雷诺数以及运动轮廓。降阶模型的解与全阶模型的解非常吻合。推力和升力在整个时间段内的误差小于0.2%。这包括复杂的场景，例如随着斯特劳哈尔数的增加，从阻力产生到推力产生的转变。与全阶模型相比，我们的时间周期降阶模型提供了从 到 到 的加速，具体取决于基础大小。这使得它成为规定时间周期问题的一个有吸引力的解决方案，并有可能通过非线性缩减技术（例如超缩减）进一步加速。