caa a22 4500 475776976 CHVBK 20180406123633.0 cr unu---uuuuu 170329e20000901xx s 000 0 eng 10.1023/A:1011138516712 doi (NATIONALLICENCE)springer-10.1023/A:1011138516712 Finite Difference Solutions of Incompressible Flow Problems with Corner Singularities [Elektronische Daten] [Huaxiong Huang, Brian Seymour] Two problems that include corner singularities are considered. The first concerns the flow of a viscous fluid in a channel driven by a constant pressure gradient, when the velocity satisfies a two-dimensional Poisson equation. The second is Stokes flow in a two-dimensional region when the stream-function satisfies the biharmonic equation. For both problems the boundaries of the domains contain corners. For corner angles greater than some critical value, the stress or the vorticity is singular. Using both a formal analysis and numerical results, we show that numerical approximations for the stream-function and velocity, obtained by using standard second-order finite difference methods, still converge to the exact solutions despite the corner singularities. However, the convergence rate is lower than second-order and the deterioration in the accuracy is not local, i.e., not confined to the corner. On the other hand, even though the vorticity solution of the Stokes problem does not converge, it diverges only locally. At a finite distance from the corner, the vorticity converges with the same rate as the stream-function. Adaptive methods for improving the accuracy are also discussed. Plenum Publishing Corporation, 2000 finite differences nationallicence corner singularities nationallicence incompressible flows nationallicence adaptive grids nationallicence asymptotic error analysis nationallicence Huang Huaxiong Department of Mathematics and Statistics, York University, M3J 1P3, Toronto, Ontario, Canada aut Seymour Brian Department of Mathematics, University of British Columbia, V6T 1Z2, Vancouver, British Columbia, Canada aut Journal of Scientific Computing Kluwer Academic Publishers-Plenum Publishers 15/3(2000-09-01), 265-292 0885-7474 15:3<265 2000 15 10915 https://doi.org/10.1023/A:1011138516712 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1023/A:1011138516712 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Huang Huaxiong Department of Mathematics and Statistics, York University, M3J 1P3, Toronto, Ontario, Canada aut NATIONALLICENCE 700 1- Seymour Brian Department of Mathematics, University of British Columbia, V6T 1Z2, Vancouver, British Columbia, Canada aut NATIONALLICENCE 773 0- Journal of Scientific Computing Kluwer Academic Publishers-Plenum Publishers 15/3(2000-09-01), 265-292 0885-7474 15:3<265 2000 15 10915 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer