%0 Journal Article %1 citeulike:14231139 %A Gresho, Philip M. %A Gartling, David K. %A Torczynski, J. R. %A Cliffe, K. A. %A Winters, K. H. %A Garratt, T. J. %A Spence, A. %A Goodrich, John W. %D 1993 %I John Wiley & Sons, Ltd %J International Journal for Numerical Methods in Fluids %K 76m22-spectral-methods-in-fluid-mechanics 76m10-finite-element-methods-in-fluid-mechanics 76m20-finite-difference-methods-in-fluid-mechanics 76e09-stability-and-instability-of-nonparallel-flows %N 6 %P 501--541 %R 10.1002/fld.1650170605 %T Is the Steady Viscous Incompressible Two-Dimensional Flow over a Backward-Facing Step at Re = 800 Stable? %U http://dx.doi.org/10.1002/fld.1650170605 %V 17 %X A detailed case study is made of one particular solution of the 2D incompressible Navier–Stokes equations. Careful mesh refinement studies were made using four different methods (and computer codes): (1) a high-order finite-element method solving the unsteady equations by time-marching; (2) a high-order finite-element method solving both the steady equations and the associated linear-stability problem; (3) a second-order finite difference method solving the unsteady equations in streamfunction form by time-marching; and (4) a spectral-element method solving the unsteady equations by time-marching. The unanimous conclusion is that the correct solution for flow over the backward-facing step at Re = 800 is steady—and it is stable, to both small and large perturbations.

@article{citeulike:14231139, abstract = {{A detailed case study is made of one particular solution of the 2D incompressible Navier–Stokes equations. Careful mesh refinement studies were made using four different methods (and computer codes): (1) a high-order finite-element method solving the unsteady equations by time-marching; (2) a high-order finite-element method solving both the steady equations and the associated linear-stability problem; (3) a second-order finite difference method solving the unsteady equations in streamfunction form by time-marching; and (4) a spectral-element method solving the unsteady equations by time-marching. The unanimous conclusion is that the correct solution for flow over the backward-facing step at Re = 800 is steady—and it is stable, to both small and large perturbations.}}, added-at = {2017-06-29T07:13:07.000+0200}, author = {Gresho, Philip M. and Gartling, David K. and Torczynski, J. R. and Cliffe, K. A. and Winters, K. H. and Garratt, T. J. and Spence, A. and Goodrich, John W.}, biburl = {https://www.bibsonomy.org/bibtex/2c581db81a4073129e31a090fd27f6787/gdmcbain}, citeulike-article-id = {14231139}, citeulike-linkout-0 = {http://dx.doi.org/10.1002/fld.1650170605}, day = 30, doi = {10.1002/fld.1650170605}, interhash = {032c52bc978e8bad5e3092f9ac82364c}, intrahash = {c581db81a4073129e31a090fd27f6787}, journal = {International Journal for Numerical Methods in Fluids}, keywords = {76m22-spectral-methods-in-fluid-mechanics 76m10-finite-element-methods-in-fluid-mechanics 76m20-finite-difference-methods-in-fluid-mechanics 76e09-stability-and-instability-of-nonparallel-flows}, month = sep, number = 6, pages = {501--541}, posted-at = {2016-12-21 04:36:33}, priority = {2}, publisher = {John Wiley \& Sons, Ltd}, timestamp = {2020-11-13T00:36:02.000+0100}, title = {Is the Steady Viscous Incompressible Two-Dimensional Flow over a Backward-Facing Step at {Re{ = 800 Stable?}}}, url = {http://dx.doi.org/10.1002/fld.1650170605}, volume = 17, year = 1993 }