Volume 5, Issue 2-4
A Third-Order Upwind Compact Scheme on Curvilinear Meshes for the Incompressible Navier-Stokes Equations

Abdullah Shah, Hong Guo & Li Yuan

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Commun. Comput. Phys., 5 (2009), pp. 712-729.

Published online: 2009-02

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  • Abstract

This paper presents a new version of the upwind compact finite difference scheme for solving the incompressible Navier-Stokes equations in generalized curvilinear coordinates. The artificial compressibility approach is used, which transforms the elliptic-parabolic equations into the hyperbolic-parabolic ones so that flux difference splitting can be applied. The convective terms are approximated by a third-order upwind compact scheme implemented with flux difference splitting, and the viscous terms are approximated by a fourth-order central compact scheme. The solution algorithm used is the Beam-Warming approximate factorization scheme. Numerical solutions to benchmark problems of the steady plane Couette-Poiseuille flow, the lid-driven cavity flow, and the constricting channel flow with varying geometry are presented. The computed results are found in good agreement with established analytical and numerical results. The third-order accuracy of the scheme is verified on uniform rectangular meshes.

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@Article{CiCP-5-712, author = {}, title = {A Third-Order Upwind Compact Scheme on Curvilinear Meshes for the Incompressible Navier-Stokes Equations}, journal = {Communications in Computational Physics}, year = {2009}, volume = {5}, number = {2-4}, pages = {712--729}, abstract = {

This paper presents a new version of the upwind compact finite difference scheme for solving the incompressible Navier-Stokes equations in generalized curvilinear coordinates. The artificial compressibility approach is used, which transforms the elliptic-parabolic equations into the hyperbolic-parabolic ones so that flux difference splitting can be applied. The convective terms are approximated by a third-order upwind compact scheme implemented with flux difference splitting, and the viscous terms are approximated by a fourth-order central compact scheme. The solution algorithm used is the Beam-Warming approximate factorization scheme. Numerical solutions to benchmark problems of the steady plane Couette-Poiseuille flow, the lid-driven cavity flow, and the constricting channel flow with varying geometry are presented. The computed results are found in good agreement with established analytical and numerical results. The third-order accuracy of the scheme is verified on uniform rectangular meshes.

}, issn = {1991-7120}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cicp/7759.html} }
TY - JOUR T1 - A Third-Order Upwind Compact Scheme on Curvilinear Meshes for the Incompressible Navier-Stokes Equations JO - Communications in Computational Physics VL - 2-4 SP - 712 EP - 729 PY - 2009 DA - 2009/02 SN - 5 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/cicp/7759.html KW - AB -

This paper presents a new version of the upwind compact finite difference scheme for solving the incompressible Navier-Stokes equations in generalized curvilinear coordinates. The artificial compressibility approach is used, which transforms the elliptic-parabolic equations into the hyperbolic-parabolic ones so that flux difference splitting can be applied. The convective terms are approximated by a third-order upwind compact scheme implemented with flux difference splitting, and the viscous terms are approximated by a fourth-order central compact scheme. The solution algorithm used is the Beam-Warming approximate factorization scheme. Numerical solutions to benchmark problems of the steady plane Couette-Poiseuille flow, the lid-driven cavity flow, and the constricting channel flow with varying geometry are presented. The computed results are found in good agreement with established analytical and numerical results. The third-order accuracy of the scheme is verified on uniform rectangular meshes.

Abdullah Shah, Hong Guo & Li Yuan. (2020). A Third-Order Upwind Compact Scheme on Curvilinear Meshes for the Incompressible Navier-Stokes Equations. Communications in Computational Physics. 5 (2-4). 712-729. doi:
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