We propose a novel artificial compression, reduced order model (AC-ROM) for the numerical simulation of viscous incompressible fluid flows. The new AC-ROM provides approximations not only for velocity, but also for pressure, which is needed to calculate forces on bodies in the flow and to connect the simulation parameters with pressure data. The new AC-ROM does not require that the velocity-pressure ROM spaces satisfy the inf-sup (Ladyzhenskaya-Babuska-Brezzi) condition and its basis functions are constructed from data that are not required to be weakly-divergence free. We prove error estimates for the reduced basis discretization of the AC-ROM. We also investigate numerically the new AC-ROM in the simulation of a two-dimensional flow between offset cylinders.

中文翻译：

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人工压缩降阶模型

我们提出了一种新的人工压缩降阶模型 (AC-ROM)，用于粘性不可压缩流体流动的数值模拟。新的 AC-ROM 不仅提供速度的近似值，还提供压力的近似值，这是计算流中物体上的力并将模拟参数与压力数据连接起来所需要的。新的 AC-ROM 不要求速度-压力 ROM 空间满足 inf-sup (Ladyzhenskaya-Babuska-Brezzi) 条件，其基函数由不需要无弱发散的数据构建。我们证明了 AC-ROM 的减少基离散化的误差估计。我们还在数值上研究了新的 AC-ROM 在偏移气缸之间的二维流动的模拟中。