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.
翻译:本条为纳维- 斯托克斯 方程式的速压分离 POD 降序模型分解提供了错误界限。 L 无限 (L 2) 和 速度的能量规范证明了稳定性,其范围不取决于粘度,而压力则以与网状尺寸的L 2 标准相同的低温半中线来证明。拟议估计数是针对两种流动问题计算的,即圆柱体流流流和柱体驱动孔流。然后用预测的对数斜度来评估其质量与速度POD 贡献比率。我们表明,拟议的误差估计可以使实际误差斜度与实际误差率的准确接近,从而对其趋同率作出良好的预测。