论文标题
连续数据同化应用于2D Navier-Stokes方程的速度涡流公式
Continuous data assimilation applied to a velocity-vorticity formulation of the 2D Navier-Stokes equations
论文作者
论文摘要
我们研究了2D Navier-Stokes方程的速度涡度公式的连续数据同化（CDA）算法，在两种情况下：裸露适用于速度和涡旋，并仅适用于速度。我们证明，在典型的有限元空间离散和向后的欧拉时间离散化下，CDA的应用保留了速度涡度方法的无条件长期稳定性属性，并提供了最佳的长时间精度。这些特性如果仅适用于速度，并且如果也将推动推动到涡度上，则可以将最佳的长时间精度及时迅速达到。数值测试说明了该理论，并显示了其在通道流过平板的应用问题上的有效性。
We study a continuous data assimilation (CDA) algorithm for a velocity-vorticity formulation of the 2D Navier-Stokes equations in two cases: nudging applied to the velocity and vorticity, and nudging applied to the velocity only. We prove that under a typical finite element spatial discretization and backward Euler temporal discretization, application of CDA preserves the unconditional long-time stability property of the velocity-vorticity method and provides optimal long-time accuracy. These properties hold if nudging is applied only to the velocity, and if nudging is also applied to the vorticity then the optimal long-time accuracy is achieved more rapidly in time. Numerical tests illustrate the theory, and show its effectiveness on an application problem of channel flow past a flat plate.
