@Article{CiCP-5-712,
author = {Abdullah Shah, Hong Guo and Li Yuan},
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 = {<p style="text-align: justify;">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.</p>},
issn = {1991-7120},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/cicp/7759.html}
}