Projection-based reduced order models rely on offline–online model decomposition, where the data-based energetic spatial basis is used in the expensive offline stage to obtain equations of reduced states that evolve in time during the inexpensive online stage. The online stage requires a solution method for the dynamic evolution of the coupled system of pressure and velocity states for incompressible fluid flows. The first contribution of this article is to demonstrate the applicability of the incremental pressure correction scheme for the dynamic evolution of pressure and velocity states. The evolution of a large number of these reduced states in the online stage can be expensive. In contrast, the accuracy significantly decreases if only a few reduced states are considered while not accounting for the interactions between unresolved and resolved states. The second contribution of this article is to compare three closure model forms based on global, modal and tensor artificial viscosity approximation to account for these interactions. The unknown model parameters are determined using two calibration techniques: least squares minimization of error in energy approximation and closure term approximation. This article demonstrates that an appropriate selection of solution methods and data-driven artificial viscosity closure models is essential for consistently accurate dynamics forecasting of incompressible fluid flows.

中文翻译：

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用于不可压缩流体流动的基于投影的降阶建模和数据驱动的人工粘度闭合

基于投影的降阶模型依赖于离线-在线模型分解，其中基于数据的能量空间基础用于昂贵的离线阶段，以获得在廉价的在线阶段随时间演化的简化状态方程。在线阶段需要一种求解不可压缩流体流动的压力和速度状态耦合系统动态演化的方法。本文的第一个贡献是证明增量压力修正方案对于压力和速度状态动态演化的适用性。在在线阶段，大量此类简化状态的演化可能代价高昂。相反，如果仅考虑一些简化状态而不考虑未解决和已解决状态之间的相互作用，则准确性会显着降低。本文的第二个贡献是比较基于全局、模态和张量人工粘度近似的三种闭合模型形式，以解释这些相互作用。使用两种校准技术确定未知模型参数：能量近似误差的最小二乘法和闭包项近似。本文证明，适当选择求解方法和数据驱动的人工粘度闭合模型对于持续准确地预测不可压缩流体流动至关重要。