On Pressure Approximation via Projection Methods for Nonstationary Incompressible Navier-Stokes Equations
On Pressure Approximation via Projection Methods for Nonstationary Incompressible Navier-Stokes Equations
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DOI：
10.1137/07069609x
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发表时间：
2008-10
期刊：
影响因子：
--
通讯作者：
A. Prohl
中科院分区：
文献类型：
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作者：
A. Prohl
投影法是逼近不可压缩Navier-Stokes方程强解的有效工具。这些方法的一个主要缺陷是，由于非物理边界数据的影响，压力迭代的精度往往会降低，同时压力迭代的误差估计也不理想。在现实的正则性假设下，我们验证了Chorin格式中边界层产生的严格界。第二步，提出了新的Chorin-Penalty方法，给出了压力迭代的最优收敛速率。
Projection methods are an efficient tool to approximate strong solutions of the incompressible Navier-Stokes equations. As a major deficiency, these methods often suffer from reduced accuracy for pressure iterates caused by nonphysical boundary data, going along with suboptimal error estimates for pressure iterates. We verify a rigorous bound for arising boundary layers in Chorin's scheme under realistic regularity assumptions. In a second step, the new Chorin-Penalty method is proposed, where optimal rate of convergence for pressure iterates is shown.