Fixing the Residual Flattening of an Upwind Compact Scheme for Steady Incompressible Flows in Enclosed Domains
Year: 2021
Author: Yunchu Wang, Li Yuan
East Asian Journal on Applied Mathematics, Vol. 11 (2021), Iss. 4 : pp. 708–731
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/eajam.281120.060421
East Asian Journal on Applied Mathematics, Vol. 11 (2021), Iss. 4 : pp. 708–731
Published online: 2021-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 24
Keywords: Incompressible Navier-Stokes equations artificial compressibility upwind compact difference convergence enclosed domain.