All Title Author
Keywords Abstract


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, PP. 35-40

Keywords: 流体混合模型;广义差分;迎风格式
Fluid Mixture Model
, Generalized Difference, Upwind Schemes

Full-Text   Cite this paper   Add to My Lib

Abstract:

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。
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.

References

[1]  M. Dembo, F. Harlow. Cell motion, constractile networks, and the physics of interpenetrating reactive flow. Biophysical Journal, 1986, 50(1): 109-121.
[2]  D. Manoussaki, S. R. Lubkin, R. B. Vernon, et al. A mechanical model for the formation of vascular networks in vitro. Acta Biotheoretica, 1996, 44(3-4): 271-282.
[3]  G. Szekely, C. Brechbuhler, R. Hutter, et al. Modelling of soft tissue deformation for laparoscopic surgery. Simulation, Medical Image Analysis, 2000, 4(1): 57-66.
[4]  W. Mollemans, F. Schutyser, J. Cleynenbreugel and P. Suetens. Tetrahedral mass spring model for fast soft tissue deformation. International Symposium on Surgery Simulation and Soft Tissue Modeling, 2003, 1673: 145-154.
[5]  S. R. Lubkin, T. Jackson. Multiphase mechanics of capsule formation in tumors. Journal of Biomechanical Engineering, 2002, 124(2): 1-7.
[6]  X. He, M. Dembo. Numerical simulation of oil-droplet cleavage by surfactant. Journal of Biomechanical Engineering, 1996, 118 (2): 201-209.
[7]  M. Stastna. A moving boundary value problem in soft tissue mechanics. Journal of Canadian Applied Mathematics Quarterly, 2005, 13(2): 183-198.
[8]  Q. Jiang, Z. Li and S. R. Lubkin. Analysis and computation for a fluid mixture model. Communication in Computational Physics, 2009, 5: 620-634.
[9]  R. Li, Z. Chen and W. Wu. Generalized difference methods for differential equation: Numerical analysis of finite volume methods. New York: Marcel Dekker, 1999.
[10]  Z. Zhang. Error estimate of finite volume element method for the pollution in ground-water flow. Numerical Method for Partial Differential Equations, 2009, 25(2): 259-274.
[11]  王平, 张志跃. 有限体积元数值方法在大气污染模式中的应用[J]. 计算物理, 2009, 26(5): 656-664.
[12]  F. Gao, Y. Yuan. The characteristic finite volume element method for the nonlinear convection-dominated diffusion problem. Computers and Mathematics with Applications, 2008, 56(1): 71- 81.
[13]  E. Richard, L. Raytcho and Y. Lin. Finite volume element approximations of nonlocal reactive flows in porous media. Numerical Method for Partial Differential Equations, 2000, 16(3): 285-311.
[14]  张文生. 科学计算中的偏微分方程有限差分法[M]. 北京: 高等教育出版社, 2006.
[15]  E. P. Doolan, J. J. H. Miller and W. H. A. Schilders. Uniform numerical methods for problems with initial and boundary layers. Dublin: Boole, 1980.

Full-Text

comments powered by Disqus

Contact Us

service@oalib.com

QQ:3279437679

微信:OALib Journal