TY - JOUR
T1 - Fixing the Residual Flattening of an Upwind Compact Scheme for Steady Incompressible Flows in Enclosed Domains
AU - Wang , Yunchu
AU - Yuan , Li
JO - East Asian Journal on Applied Mathematics
VL - 4
SP - 708
EP - 731
PY - 2021
DA - 2021/08
SN - 11
DO - http://doi.org/10.4208/eajam.281120.060421
UR - https://global-sci.org/intro/article_detail/eajam/19369.html
KW - Incompressible Navier-Stokes equations, artificial compressibility, upwind compact difference, convergence, enclosed domain.
AB - <p style="text-align: justify;">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.</p>