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Numerical methods for a fluid mixture model
Author(s) -
Wang Quanxiang,
Lin Suli,
Zhang Zhiyue
Publication year - 2012
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.3639
Subject(s) - mathematics , upwind scheme , finite difference method , finite difference , convergence (economics) , nonlinear system , space (punctuation) , mathematical analysis , partial differential equation , galerkin method , function (biology) , elliptic curve , numerical analysis , computer science , discretization , physics , quantum mechanics , evolutionary biology , economics , biology , economic growth , operating system
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.