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A Stable and Convergent Finite Difference Scheme for 2D Incompressible Nonlinear Viscoelastic Fluid Dynamics Problem
Applied and Computational Mathematics
Volume 7, Issue 1, February 2018, Pages: 11-18
Received: Dec. 4, 2017; Accepted: Dec. 15, 2017; Published: Jan. 12, 2018
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Yanhua Cao, School of Sciences, East China Jiaotong University, Nanchang, China
Zhendong Luo, School of Mathematics and Physics, North China Electric Power University, Beijing, China
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In this study, a stable and convergent finite difference (FD) scheme based on staggered meshes for two-dimensional (2D) incompressible nonlinear viscoelastic fluid dynamics problem including the velocity vector field and the pressure field as well as the deformation tensor matrix is established in order to find numerical solutions for the problem. The stability, convergence, and errors of the FD solutions are analyzed. Some numerical experiments are presented to show that the FD scheme is feasible and efficient for simulating the phenomena of the velocity and the pressure as well as the deformation tensor in an estuary.
Finite Difference Scheme, Incompressible Nonlinear Viscoelastic Fluid Problem, Stability and Convergence, Numerical Simulations
To cite this article
Yanhua Cao, Zhendong Luo, A Stable and Convergent Finite Difference Scheme for 2D Incompressible Nonlinear Viscoelastic Fluid Dynamics Problem, Applied and Computational Mathematics. Vol. 7, No. 1, 2018, pp. 11-18. doi: 10.11648/j.acm.20180701.12
Copyright © 2018 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License ( which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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