论文标题
Navier-Stokes方程的正确正交分解数据同化方案的错误分析
Error analysis of proper orthogonal decomposition data assimilation schemes for the Navier-Stokes equations
论文作者
论文摘要
对Navier-Stokes方程的适当正交分解（POD）数据同化（DA）方程的误差分析进行了。将毕业划线稳定项添加到POD方法的配方中。与粘度参数的逆强度独立于POD算法的逆向力的误差边界。在数据同化方法的淡淡参数中不需要上限。数值实验表明，对于小推动参数的大量值，所提出的方法迅速收敛到实际解决方案，并大大提高了标准POD方案的总体准确性，高于预测时间间隔的低粘度。
The error analysis of a proper orthogonal decomposition (POD) data assimilation (DA) scheme for the Navier-Stokes equations is carried out. A grad-div stabilization term is added to the formulation of the POD method. Error bounds with constants independent on inverse powers of the viscosity parameter are derived for the POD algorithm. No upper bounds in the nudging parameter of the data assimilation method are required. Numerical experiments show that, for large values of the nudging parameter, the proposed method rapidly converges to the real solution, and greatly improves the overall accuracy of standard POD schemes up to low viscosities over predictive time intervals.
