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Volume 6, Issue 3
Dimension Splitting Method for 3D Rotating Compressible Navier-Stokes Equations in the Turbomachinery

K. Li & D. Liu

Int. J. Numer. Anal. Mod., 6 (2009), pp. 420-439.

Published online: 2009-06

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  • Abstract

In this paper, we propose a dimension splitting method for Navier-Stokes equations (NSEs). The main idea is as follows. The domain of flow in 3D is decomposed into several thin layers. In each layer, The 3D NSEs can be represented as the sum of a membrane operator and a normal (bending) operator on the boundary of layer. And The Euler central difference is used to approximate the bending operator. When restricting the 3D NSEs on the boundary in each layer, we obtain a series of two dimensional-three components NSEs (called as 2D-3C NSEs). Then we construct an approximate solution of 3D NSES by solutions of those 2D-3C NSEs.

  • Keywords

2D manifold, semi-geodesic coordinate Navier-Stokes equations, dimension splitting method.

  • AMS Subject Headings

35R35, 49J40, 60G40

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-6-420, author = {K. Li and D. Liu}, title = {Dimension Splitting Method for 3D Rotating Compressible Navier-Stokes Equations in the Turbomachinery}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2009}, volume = {6}, number = {3}, pages = {420--439}, abstract = {

In this paper, we propose a dimension splitting method for Navier-Stokes equations (NSEs). The main idea is as follows. The domain of flow in 3D is decomposed into several thin layers. In each layer, The 3D NSEs can be represented as the sum of a membrane operator and a normal (bending) operator on the boundary of layer. And The Euler central difference is used to approximate the bending operator. When restricting the 3D NSEs on the boundary in each layer, we obtain a series of two dimensional-three components NSEs (called as 2D-3C NSEs). Then we construct an approximate solution of 3D NSES by solutions of those 2D-3C NSEs.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/776.html} }
TY - JOUR T1 - Dimension Splitting Method for 3D Rotating Compressible Navier-Stokes Equations in the Turbomachinery AU - K. Li & D. Liu JO - International Journal of Numerical Analysis and Modeling VL - 3 SP - 420 EP - 439 PY - 2009 DA - 2009/06 SN - 6 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/776.html KW - 2D manifold, semi-geodesic coordinate Navier-Stokes equations, dimension splitting method. AB -

In this paper, we propose a dimension splitting method for Navier-Stokes equations (NSEs). The main idea is as follows. The domain of flow in 3D is decomposed into several thin layers. In each layer, The 3D NSEs can be represented as the sum of a membrane operator and a normal (bending) operator on the boundary of layer. And The Euler central difference is used to approximate the bending operator. When restricting the 3D NSEs on the boundary in each layer, we obtain a series of two dimensional-three components NSEs (called as 2D-3C NSEs). Then we construct an approximate solution of 3D NSES by solutions of those 2D-3C NSEs.

K. Li and D. Liu. (2009). Dimension Splitting Method for 3D Rotating Compressible Navier-Stokes Equations in the Turbomachinery. International Journal of Numerical Analysis and Modeling. 6 (3). 420-439. doi:
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