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Moving Mesh Finite Element Method for Unsteady Navier-Stokes Flow

Part of:Partial differential equations, initial value and time-dependent initial-boundary value problems

Published online by Cambridge University Press:  17 January 2017

Yirong Wu and
Heyu Wang
Yirong Wu*
Affiliation:
School of Mathematical Science, Zhejiang University, HangZhou, Zhejiang 310027, China
Heyu Wang*
Affiliation:
School of Mathematical Science, Zhejiang University, HangZhou, Zhejiang 310027, China
*
*Corresponding author. Email:wuwuyiyirongrong@163.com (Y. R. Wu), wang.heyu@gmail.com (H. Y.Wang)
*Corresponding author. Email:wuwuyiyirongrong@163.com (Y. R. Wu), wang.heyu@gmail.com (H. Y.Wang)

Abstract

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In this paper, we use moving mesh finite element method based upon 4P 1–P 1 element to solve the time-dependent Navier-Stokes equations in 2D. Two-layer nested meshes are used including velocity mesh and pressure mesh, and velocity mesh can be obtained by globally refining pressure mesh. We use hierarchy geometry tree to store the nested meshes. This data structure make convienence for adaptive mesh method and the construction of multigrid preconditioning. Several numerical problems are used to show the effect of moving mesh.

Keywords

Navier-Stokes system4P 1–P 1hierarchy geometry treemoving mesh method

MSC classification

Secondary:65M60: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods

Information

Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 9 , Issue 3 , June 2017, pp. 742 - 756
Copyright
Copyright © Global-Science Press 2017 

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