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Convergence analysis of an implicit fractional-step method for the incompressible Navier-Stokes equations

机译:不可压缩的Navier-Stokes方程的隐式分数步法的收敛性分析

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In this paper, an implicit fractional-step method for numerical solutions of the incompressible Navier-Stokes equations is studied. The time advancement is decomposed into a sequence of two steps, and the first step can be seen as a linear elliptic problem; on the other hand, the second step has the structure of the Stokes problem. The two problems satisfy the full homogeneous Dirichlet boundary conditions on the velocity. At the same time, we introduce a diffusion term -0Δu in all steps of the schemes. It allows to calculate by the large time step and enhance numerical stability by choosing the proper parameter values of 0. The convergence analysis and error estimates for the intermediate velocities, the end-of step velocities and the pressure solution are derived. Finally, numerical experiments show that the feasibility and effectiveness of this method.
机译:本文研究了不可压缩的Navier-Stokes方程数值解的隐式分数步法。时间提前量被分解为两个步骤,第一步可以看作是线性椭圆问题。另一方面,第二步具有斯托克斯问题的结构。这两个问题满足了速度上完全齐次Dirichlet边界条件。同时,我们在方案的所有步骤中引入了扩散项-0Δu。它允许以较大的时间步长进行计算,并通过选择适当的参数值0来增强数值稳定性。得出了中间速度,步长结束速度和压力解的收敛性分析和误差估计。最后,数值实验表明了该方法的可行性和有效性。

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