The a priori error analysis of reduced order models (ROMs) for fluids is relatively scarce. In this paper, we take a step in this direction and conduct numerical analysis of the recently introduced time relaxation ROM (TR-ROM), which uses spatial filtering to stabilize ROMs for convection-dominated flows. Specifically, we prove stability, an a priori error bound, and parameter scalings for the TR-ROM. Our numerical investigation shows that the theoretical convergence rate and the parameter scalings with respect to ROM dimension and filter radius are recovered numerically. In addition, the parameter scaling can be used to extrapolate the time relaxation parameter to other ROM dimensions and filter radii. Moreover, the parameter scaling with respect to filter radius is also observed in the predictive regime.

翻译：流体降阶模型（ROM）的先验误差分析相对匮乏。本文在此方向上迈出一步，对近期提出的时间松弛降阶模型（TR-ROM）进行数值分析，该模型利用空间滤波技术稳定对流主导流动的降阶模型。具体而言，我们证明了TR-ROM的稳定性、先验误差界及参数尺度律。数值研究表明，理论收敛率以及关于ROM维数与滤波半径的参数尺度律均得到数值验证。此外，该参数尺度律可用于将时间松弛参数外推至其他ROM维数与滤波半径。更重要的是，关于滤波半径的参数尺度律在预测域中同样得到观测。