应用物理  >> Vol. 2 No. 2 (April 2012)

一类流体混合模型的广义差分法
Generalized Difference Methods for a Fluid Mixture Model

DOI: 10.12677/app.2012.22006, PDF, HTML,  被引量 下载: 3,000  浏览: 8,102  国家自然科学基金支持

作者: 林素丽, 王全祥, 张志跃:南京师范大学数学科学学院

关键词: 流体混合模型广义差分迎风格式
Fluid Mixture Model; Generalized Difference; Upwind Schemes

摘要: 本文针对一类流体混合模型设计了两种数值格式。该流体混合模型是关于可收缩间叶细胞组织变形的模型,是由非线性的双曲型方程和椭圆型方程组成的混合方程组。第一种方法通过选取试探函数空间和检验函数空间为一次元函数空间和分片常函数空间,针对光滑情形,得到的广义差分格式具有二阶精度。为消除解在间断处的数值震荡,我们设计求解该流体混合模型的广义迎风差分格式。数值结果表明两种数值方法对考虑的混合模型是有效的。
Abstract: In this paper, we propose two numerical methods for a fluid mixture model. The model is usually used to describe the tissue deformations. It contains a nonlinear hyperbolic equation and an elliptic equation. The first numerical method is the generalized difference method based on linear element function space and piecewise constant function space. Numerical experiments show that our scheme is second-order accuracy in space. To eliminate the oscillation near the discontinuities, we design a generalized upwind difference method to solve the fluid model. Numerical results show that the two methods are effective for the considered fluid mixture model.

文章引用: 林素丽, 王全祥, 张志跃. 一类流体混合模型的广义差分法[J]. 应用物理, 2012, 2(2): 35-40. http://dx.doi.org/10.12677/app.2012.22006

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