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Volume 9, Issue 3
Moving Mesh Finite Element Method for Unsteady Navier-Stokes Flow

Yirong Wu & Heyu Wang

DOI: 10.4208/aamm.2016.m1457

Adv. Appl. Math. Mech., 9 (2017), pp. 742-756.

Published online: 2018-05

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  • Abstract

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 provides convenience 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 system, $4P_1−P_1$, hierarchy geometry tree, moving mesh method.

  • AMS Subject Headings

65M60

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-9-742, author = {Wu , Yirong and Wang , Heyu}, title = {Moving Mesh Finite Element Method for Unsteady Navier-Stokes Flow}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2018}, volume = {9}, number = {3}, pages = {742--756}, abstract = {

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 provides convenience for adaptive mesh method and the construction of multigrid preconditioning. Several numerical problems are used to show the effect of moving mesh.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.2016.m1457}, url = {http://global-sci.org/intro/article_detail/aamm/12173.html} }
TY - JOUR T1 - Moving Mesh Finite Element Method for Unsteady Navier-Stokes Flow AU - Wu , Yirong AU - Wang , Heyu JO - Advances in Applied Mathematics and Mechanics VL - 3 SP - 742 EP - 756 PY - 2018 DA - 2018/05 SN - 9 DO - http://doi.org/10.4208/aamm.2016.m1457 UR - https://global-sci.org/intro/article_detail/aamm/12173.html KW - Navier-Stokes system, $4P_1−P_1$, hierarchy geometry tree, moving mesh method. AB -

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 provides convenience for adaptive mesh method and the construction of multigrid preconditioning. Several numerical problems are used to show the effect of moving mesh.

Wu , Yirong and Wang , Heyu. (2018). Moving Mesh Finite Element Method for Unsteady Navier-Stokes Flow. Advances in Applied Mathematics and Mechanics. 9 (3). 742-756. doi:10.4208/aamm.2016.m1457
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