In this paper, we develop data-driven closure/correction terms to increase the pressure and velocity accuracy of reduced order models (ROMs) for fluid flows. Specifically, we propose the first pressure-based data-driven variational multiscale ROM, in which we use the available data to construct closure/correction terms for both the momentum equation and the continuity equation. Our numerical investigation of the two-dimensional flow past a circular cylinder at Re=50000 in the marginally-resolved regime shows that the novel pressure data-driven variational multiscale ROM yields significantly more accurate velocity and pressure approximations than the standard ROM and, more importantly, than the original data-driven variational multiscale ROM (i.e., without pressure components). In particular, our numerical results show that adding the closure/correction term in the momentum equation significantly improves both the velocity and the pressure approximations, whereas adding the closure/correction term in the continuity equation improves only the pressure approximation.

翻译：在本文中,我们开发了数据驱动的封闭/校正术语,以提高流体减序模型(ROMs)的压力和速度精确度。具体地说,我们提出了第一个基于压力的数据驱动多比例变式模型(ROMs),其中我们使用可用数据构建动力方程式和连续性方程式的封闭/校正术语。我们对微溶解系统中以Re=50000为值的双维圆柱体流进行的数字调查表明,新的压力数据驱动的多尺度变式ROM比标准ROM的更精确的速度和压力近似值,更重要的是,比原数据驱动的多比例变式ROM(即没有压力组件)要高得多。特别是,我们的数字结果显示,在动力方程式中添加封闭/校正术语,大大改进了速度和压力近似值,而在连续性方程式中添加关闭/校正术语只改进了压力逼近值。