Numerical methods for a fluid mixture model

Authors

  • Quanxiang Wang,

    1. Jiangsu Provincial Key Laboratory for Numerical Simulation of Large Scale Complex Systems, School of Mathematical Sciences, Nanjing Normal University, Nanjing, China
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  • Suli Lin,

    1. Jiangsu Provincial Key Laboratory for Numerical Simulation of Large Scale Complex Systems, School of Mathematical Sciences, Nanjing Normal University, Nanjing, China
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  • Zhiyue Zhang

    Corresponding author
    • Jiangsu Provincial Key Laboratory for Numerical Simulation of Large Scale Complex Systems, School of Mathematical Sciences, Nanjing Normal University, Nanjing, China
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Zhiyue Zhang, Jiangsu Provincial Key Laboratory for Numerical Simulation of Large Scale Complex Systems, School of Mathematical Sciences, Nanjing Normal University, Nanjing 210046, China.

E-mail: zhangzhiyue@njnu.edu.cn

SUMMARY

In this paper, we firstly apply generalized difference methods to solve a fluid mixture model. The model is usually used to describe the tissue deformations and contains a nonlinear hyperbolic equation and an elliptic equation. Most people have used finite difference methods for solving the elliptic equation and other schemes for solving the hyperbolic equation. It is well known that the accuracy of traditional finite difference method is not high. This may be a serious disadvantage in the fluid mixture model, which describes cell movements and tissue deformations. The numerical methods we propose to improve accuracy are based on generalized Galerkin methods and dual decomposition. By choosing suitable trial function space and test function space, our generalized upwind difference schemes exhibit second-order convergence in space for smooth problems and can eliminate numerical oscillations for discontinuous problems. Some numerical results are presented to demonstrate the advantages of our methods. Copyright © 2012 John Wiley & Sons, Ltd.

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