On a multi-scale element-free Galerkin method for the Stokes problem
On a multi-scale element-free Galerkin method for the Stokes problem
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DOI：
10.1016/j.amc.2008.05.081
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发表时间：
2008-09
期刊：
影响因子：
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通讯作者：
Lin Zhang;J. Ouyang;Xiaohua Zhang;Wenbin Zhang
中科院分区：
文献类型：
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作者：
Lin Zhang;J. Ouyang;Xiaohua Zhang;Wenbin Zhang
本文提出了一种求解Stokes问题的多尺度无单元Galerkin方法。新方法基于Hughes的变分多尺度公式，将速度场分解为粗/分辨尺度和细/未分辨尺度。在这种方法中，未解决的模型中，未解决的尺度分析纳入通过气泡功能。未解决的尺度的建模纠正了缺乏稳定性的标准无单元Galerkin制定和由此产生的稳定制定具有上级属性一样，流线迎风/彼得罗夫-Galerkin（SUPG）方法和Galerkin/最小二乘（GLS）方法。由于该方法违反了著名的Babuska-Brezzi条件，因此允许压力和速度的等阶基。本方法的一个显著特点是通过精细尺度问题的求解自然地呈现稳定张量τ的结构。算例结果表明，该方法具有较好的稳定性和精度。
In this paper, a multi-scale element-free Galerkin method is presented for the Stokes problem. The new method is based on the Hughes’ variational multi-scale formulation, and arises from a decomposition of the velocity field into coarse/resolved scales and fine/unresolved scales. In this method, an unresolved model is obtained in which unresolved scales are incorporated analytically through the bubble functions. Modeling of the unresolved scales corrects the lack of the stability of the standard element-free Galerkin formulation and the resulting stabilized formulation possesses superior properties like that of the streamline upwind/Petrov–Galerkin (SUPG) method and the Galerkin/least-squares (GLS) method. The method allows equal order basis for pressure and velocity because it violates the celebrated Babuska–Brezzi condition. A significant feature of the present method is that the structure of the stabilization tensor τ appears naturally via the solution of the fine-scale problem. Numerical results for example problems confirm that this method has some excellent properties, such as better stability and accuracy.