论文标题
不可压缩流的完全离散增量投影方案的收敛
Convergence of the fully discrete incremental projection scheme for incompressible flows
论文作者
论文摘要
本文介绍了时间相关的不可压缩的Navier-Stokes方程与弱解决方案的一阶递增投影方案的收敛性，而没有任何存在或定期假设在确切解决方案上的假设。我们证明了通过半二聚体方案获得的近似解决方案的收敛性和使用交错的有限体积方案在非均匀矩形网格上获得的完全离散的方案。一些关于近似解决方案的先验估计值首先产生的。紧凑型参数，依靠这些估计值，以及对离散时间衍生物的翻译的一些估计，然后开发出来以获得收敛（直至在半差异方案中的时间步骤趋向于零，以及空间和时间步骤在完全离散方案中趋于零时；因此，近似解决方案被证明会收敛到极限函数，然后通过传递到这些方案中的极限来表明对连续问题的弱解决方案。
The present paper addresses the convergence of a first order in time incremental projection scheme for the time-dependent incompressible Navier-Stokes equations to a weak solution, without any assumption of existence or regularity assumptions on the exact solution. We prove the convergence of the approximate solutions obtained by the semi-discrete scheme and a fully discrete scheme using a staggered finite volume scheme on non uniform rectangular meshes. Some first a priori estimates on the approximate solutions yield the existence. Compactness arguments, relying on these estimates, together with some estimates on the translates of the discrete time derivatives, are then developed to obtain convergence (up to the extraction of a subsequence), when the time step tends to zero in the semi-discrete scheme and when the space and time steps tend to zero in the fully discrete scheme; the approximate solutions are thus shown to converge to a limit function which is then shown to be a weak solution to the continuous problem by passing to the limit in these schemes.
