An algebraic variational multiscale-multigrid method based on plain aggregation for convection-diffusion problems
An algebraic variational multiscale-multigrid method based on plain aggregation for convection-diffusion problems
复制标题
解决对流扩散问题的基于平面聚合的代数变分多尺度多重网格方法
DOI：
10.1016/j.cma.2009.08.017
复制
发表时间：
2009
影响因子：
7.2
通讯作者：
W. Wall
中科院分区：
文献类型：
--
作者：
V. Gravemeier;M. W. Gee;W. Wall
提出了一种新的计算框架，称为代数变分多尺度多重网格方法，代表我们的工作的第一步合并变分多尺度方法与代数多重网格投影方法。这种新的方法允许一个分离的解决规模到各种规模组在一个纯粹的代数方式，也就是说，没有必要利用进一步的离散化超出了基本的。通过这种方式，它方便地促进了建模项应用于所有尺度组或仅应用于选定的尺度组，例如仅应用于问题的精细尺度。变分多重网格技术形成了我们的新方法的基础。在提出一个抽象的问题制定的框架的基石，变分多尺度方法的投影方法一般和变分多重网格技术的密切关系进行了讨论。然后详细分析了对流扩散问题的代数变分多尺度多重网格方法。目前的初步研究重点是开发一个精细尺度的不连续性捕获方法，以减少在尖锐层的振荡，利用新框架的方法方面。我们的技术，包括一个细尺度的不连续捕捉项被应用到强对流为主的对流扩散问题的数值例子。结果表明，它能使抛物边界层和内层的局部振荡减小约60-80%，而没有任何明显的涂抹效应。
A new computational framework referred to as algebraic variational multiscale–multigrid method is proposed, representing the initial step of our work on merging the variational multiscale method with algebraic multigrid projection methods. This new approach allows for a separation of resolved scales into various scale groups in a purely algebraic way, that is, with no need to utilize further discretizations beyond the basic one. By this means, it conveniently facilitates the application of modeling terms either to all scale groups or only to selected scale groups, for instance, only to the fine scales of the problem. Variational multigrid techniques form the basis of our new approach. After presenting the cornerstones of the framework for an abstract problem formulation, the close relationship of the variational multiscale method to projection methods in general and to variational multigrid techniques are discussed. The algebraic variational multiscale–multigrid method is then particularly analyzed for convection–diffusion problems. The present initial study focuses on exploiting the methodical aspects of the new framework by developing a fine-scale discontinuity-capturing approach to diminish oscillations at sharp layers. Our technique including a fine-scale discontinuity-capturing term is applied to numerical examples of strongly convection-dominated convection–diffusion problems. The results demonstrate that it enables the diminuation of local oscillations at parabolic boundary and interior layers by about 60–80% without any notable smearing effect.