East Asian J. Appl. Math., 11 (2021), pp. 708-731.
Published online: 2021-08
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The iterative convergence of the upwind compact finite difference scheme for the artificial compressibility method [A. Shah et al, A third-order upwind compact scheme on curvilinear meshes for the incompressible Navier-Stokes equations, Commun. Comput. Phys. 5 (2009)] is studied. It turns out that for steady flows in enclosed domains the residuals do not converge to machine zero. The reason is a non-uniqueness of the calculated pressure in the case where Neumann boundary conditions for the pressure are imposed on all boundaries. The problem can be fixed by modifying the derivatives of mass flux obtained from the upwind compact scheme to satisfy the global mass conservation constraint. Numerical tests show that with this modification the scheme converges to machine zero with the original third-order accuracy.
}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.281120.060421}, url = {http://global-sci.org/intro/article_detail/eajam/19369.html} }The iterative convergence of the upwind compact finite difference scheme for the artificial compressibility method [A. Shah et al, A third-order upwind compact scheme on curvilinear meshes for the incompressible Navier-Stokes equations, Commun. Comput. Phys. 5 (2009)] is studied. It turns out that for steady flows in enclosed domains the residuals do not converge to machine zero. The reason is a non-uniqueness of the calculated pressure in the case where Neumann boundary conditions for the pressure are imposed on all boundaries. The problem can be fixed by modifying the derivatives of mass flux obtained from the upwind compact scheme to satisfy the global mass conservation constraint. Numerical tests show that with this modification the scheme converges to machine zero with the original third-order accuracy.