A variational multiscale Newton–Schur approach for the incompressible Navier–Stokes equations
A variational multiscale Newton–Schur approach for the incompressible Navier–Stokes equations
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不可压缩纳维-斯托克斯方程的变分多尺度牛顿-舒尔方法
DOI：
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发表时间：
2008
期刊：
影响因子：
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通讯作者：
K. Hjelmstad
中科院分区：
文献类型：
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作者：
D. Turner;K. Nakshatrala;K. Hjelmstad
在本文中，我们给出了三维含时N-S方程变分多尺度方程的相容牛顿-舒尔(NS)解方法。这项工作的主要贡献是对三维问题的变分多尺度方法进行了系统的研究，并实现了适用于具有高度非线性、非结构网格和非对称矩阵的大型问题的一致格式。除了基于牛顿-拉夫森格式的二次收敛特性外，NS方法还通过以Schur补的形式实现切线刚度矩阵来提高计算效率和并行可伸缩性。因此，在元素级别执行更多的计算。利用变分多尺度框架，我们构造了一个基于粗细尺度子问题的两层方法来稳定化不可压缩的N-S方程。然后，我们推导出相切矩阵的Schur补形式。在雷诺数为1000的三维问题中，我们展示了该方法的性能，包括定常流动和随时间变化的流动。版权所有©2009 John Wiley&Sons，Ltd.
In the following paper, we present a consistent Newton–Schur (NS) solution approach for variational multiscale formulations of the time‐dependent Navier–Stokes equations in three dimensions. The main contributions of this work are a systematic study of the variational multiscale method for three‐dimensional problems and an implementation of a consistent formulation suitable for large problems with high nonlinearity, unstructured meshes, and non‐symmetric matrices. In addition to the quadratic convergence characteristics of a Newton–Raphson‐based scheme, the NS approach increases computational efficiency and parallel scalability by implementing the tangent stiffness matrix in Schur complement form. As a result, more computations are performed at the element level. Using a variational multiscale framework, we construct a two‐level approach to stabilizing the incompressible Navier–Stokes equations based on a coarse and fine‐scale subproblem. We then derive the Schur complement form of the consistent tangent matrix. We demonstrate the performance of the method for a number of three‐dimensional problems for Reynolds number up to 1000 including steady and time‐dependent flows. Copyright © 2009 John Wiley & Sons, Ltd.