Preconditioning for the Steady-State Navier-Stokes Equations with Low Viscosity
Preconditioning for the Steady-State Navier-Stokes Equations with Low Viscosity
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DOI：
10.1137/s1064827596312547
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发表时间：
1999-02
期刊：
影响因子：
--
通讯作者：
H. Elman
中科院分区：
文献类型：
--
作者：
H. Elman
我们为线性化的Navier-Stokes方程引入了一种预条件算子，它在离散网格尺寸或粘性趋于零时是有效的。对于具有周期边界条件的常系数问题，我们证明了预条件可以得到一个单一本征值等于1的系统，因此性能与粘性和网格大小无关。对于其他边界条件，我们经验地证明了收敛仅温和地依赖于这些参数，并对这一现象进行了部分分析。我们还表明，新方法所需的一些昂贵的辅助计算可以被基于迭代的这些任务的廉价近似版本所取代，而几乎不会降低性能。
We introduce a preconditioner for the linearized Navier--Stokes equations that is effective when either the discretization mesh size or the viscosity approaches zero. For constant coefficient problems with periodic boundary conditions, we show that the preconditioning yields a system with a single eigenvalue equal to 1, so that performance is independent of both viscosity and mesh size. For other boundary conditions, we demonstrate empirically that convergence depends only mildly on these parameters and we give a partial analysis of this phenomenon. We also show that some expensive subsidiary computations required by the new method can be replaced by inexpensive approximate versions of these tasks based on iteration, with virtually no degradation of performance.