低磁雷诺数磁流体的 Grad-Div 稳定有限元法

IF 1.2 3区 数学 Q2 MATHEMATICS, APPLIED
Yao Rong, Feng Shi, Yi Li, Yuhong Zhang
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引用次数: 0

摘要

不可压缩流体的发散约束往往导致标准混合有限元方法鲁棒性较弱。梯度镇定是一种常用的提高鲁棒性的技术。本文从理论上证明,对于大哈特曼数的磁流体动力学流动,梯度镇定可以改善连续问题的适定性和鲁棒稳定性,消除哈特曼数对有限元离散误差的影响。此外,应用后向欧拉法,对非线性项进行滞后,构造了低磁雷诺数下磁流体力学流动的线性梯度稳定有限元算法。对其稳定性和收敛性进行了完整的理论分析。一些计算实验证明了算法的有效性和理论结果,以及梯度稳定的优点。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

Grad-Div Stabilized Finite Element Method for Magnetohydrodynamic Flows at Low Magnetic Reynolds Numbers

Grad-Div Stabilized Finite Element Method for Magnetohydrodynamic Flows at Low Magnetic Reynolds Numbers

The divergence constraint of the incompressible fluids usually causes the weak robustness of standard mixed finite element methods. Grad-div stabilization is a popular technique for improving the robustness. In this paper, we theoretically show that for magnetohydrodynamic flows at large Hartmann numbers, grad-div stabilization can improve the well-posedness and robust stability of the continuous problem, and remove the effect of Hartmann number on the finite element discrete errors. Besides, applying the backward Euler method and lagging the nonlinear term, we construct a linear grad-div stabilized finite element algorithm for magnetohydrodynamics flows at low magnetic Reynolds numbers. A complete theoretical analysis of its stability and convergency is provided. Some computational experiments illustrate the validness of our algorithm and its theoretical results and also the benefits of grad-div stabilization.

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来源期刊
CiteScore
2.00
自引率
15.40%
发文量
97
审稿时长
>12 weeks
期刊介绍: The Journal of Mathematical Fluid Mechanics (JMFM)is a forum for the publication of high-quality peer-reviewed papers on the mathematical theory of fluid mechanics, with special regards to the Navier-Stokes equations. As an important part of that, the journal encourages papers dealing with mathematical aspects of computational theory, as well as with applications in science and engineering. The journal also publishes in related areas of mathematics that have a direct bearing on the mathematical theory of fluid mechanics. All papers will be characterized by originality and mathematical rigor. For a paper to be accepted, it is not enough that it contains original results. In fact, results should be highly relevant to the mathematical theory of fluid mechanics, and meet a wide readership.
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