论文标题
对不可压缩流的残余稳定动机动机的POD-ROM的错误分析
Error analysis of a residual-based stabilization-motivated POD-ROM for incompressible flows
论文作者
论文摘要
本文介绍了速度压力隔离的POD的错误界限，降低了Navier-Stokes方程的订单模型离散化。稳定性在L Infinity（L 2）和速度的能量规范中得到了证明，其边界不取决于粘度，而对于压力，它在与网格大小相对于L 2标准的半标记中被证明。提出的估计值是针对两个流问题的计算，即经过气缸和盖子驱动的腔流。然后，根据速度POD贡献比的预测对数斜率评估它们的质量。我们表明，提出的误差估计值允许对真实误差斜率进行良好的近似，从而可以很好地预测其收敛速度。
This article presents error bounds for a velocity-pressure segregated POD reduced order model discretization of the Navier-Stokes equations. The stability is proven in L infinity (L 2 ) and energy norms for velocity, with bounds that do not depend on the viscosity, while for pressure it is proven in a semi-norm of the same asymptotic order as the L 2 norm with respect to the mesh size. The proposed estimates are calculated for the two flow problems, the flow past a cylinder and the lid-driven cavity flow. Their quality is then assessed in terms of the predicted logarithmic slope with respect to the velocity POD contribution ratio. We show that the proposed error estimates allow a good approximation of the real errors slopes and thus a good prediction of their rate of convergence.
