Quadratic, streamline upwinding for finite element method solutions to 2-D convective transport problems
Quadratic, streamline upwinding for finite element method solutions to 2-D convective transport problems
复制标题
二维对流传输问题的有限元法解决方案的二次、流线型逆风
DOI：
10.1016/0045-7825(96)01026-2
复制
发表时间：
1996
影响因子：
7.2
通讯作者：
B. Deblois
中科院分区：
文献类型：
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作者：
B. Deblois
在过去的十年中，有限元方法（FEM）已被公认为是更强大的工具，在解决各种流动问题，而不是他们的前辈，有限差分方法。在基本层面上，FEM涉及离散网格上给定试验空间上的解的近似，而不是离散网格上微分算子的有限差分近似。通过这种方式，FEM的力学（操作员）更接近与给定问题相关的物理原理。除此之外，FEM将边界条件非常有效地结合到数值公式中。目前的许多研究旨在使这些有限元法可行的选择对流为主的流动。1985年，Mizukami等人发表了两篇论文，提出了有限元线性单元内流线上溯的方法。这项工作的目的是证明，流线迎风高阶元素是一个更准确的选择。这项工作继续显示究竟如何流线迎风效果的稳定性迭代求解的全球代数系统所产生的有限元法。
During the past decade, Finite Element Methods (FEMs) have been recognized to be more powerful tools in the solution of various flow problems as opposed to their predecessors, Finite Difference Methods. On a fundamental level, the FEM involves approximations to the solution over a given trial space on a discrete mesh, rather than Finite Difference approximations to the differential operators on a discrete mesh. In this way, the mechanics (operators) of the FEM remain closer to the physical principles associated with a given problem. In addition to this, the FEM incorporates boundary conditions very efficiently into the numerical formulation. Much current research is aimed at making these FEMs viable options for convection-dominated flows. In 1985, Mizukami et al. published two papers advancing the approach of streamline upwinding within linear elements for FEMs. The purpose of this work is to demonstrate that streamline upwinding of higher ordered elements is a more accurate option. The work goes on to show exactly how streamline upwinding effects the stability of iteratively solving the global algebraic system resulting from the FEM.