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On discrete projection and numerical boundary conditions for the numerical solution of the unsteady incompressible navier-stokes equations

机译:关于非定常不可压缩Navier-stokes方程数值解的离散投影和数值边界条件

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The unsteady incompressible Navier-Stokes equations are discretized in space and stud- ied on the fixed mesh as a system of differential algebraic equations. With discrete project- tion defined, the local errors of Crank Nicholson schemes with three projection methods are derived in a straightforward manner. Then the approximate factorization of relevant matrices are used to study the time accuracy with more detail, especially at points adjacent to the boundary. The effects of numerical boundary conditions of the auxiliary velocity and the discrete pressure Poisson equation on the time accuracy are also investigated. Re- sults of numerical experiments with an analytic example confirm the conclusions of our analysis.
机译:非定常不可压缩的Navier-Stokes方程在空间上离散,并作为微分代数方程组学习在固定网格上。在定义了离散投影的情况下,以三种简单的方法可以得出Crank Nicholson方案的局部误差。然后使用相关矩阵的近似因式分解来更详细地研究时间精度,尤其是在边界附近的点。还研究了辅助速度和离散压力泊松方程的数值边界条件对时间精度的影响。数值实验的结果和一个解析例子证实了我们分析的结论。

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