%0 Journal Article %1 shih1989effects %A Shih, T. M. %A Tan, C. H. %A Hwang, B. C. %D 1989 %I John Wiley & Sons, Ltd %J International Journal for Numerical Methods in Fluids %K incompressible mms verification %N 2 %P 193--212 %R 10.1002/fld.1650090206 %T Effects of grid staggering on numerical schemes %U http://dx.doi.org/10.1002/fld.1650090206 %V 9 %X Nine finite difference schemes using primitive variables on various grid arrangements were systematically tested on a benchmark problem of two-dimensional incompressible Navier–Stokes flows. The chosen problem is similar to the classical lid-driven cavity flow, but has a known exact solution. Also, it offers the reader an opportunity to thoroughly evaluate accuracies of various conceptual grid arrangements.Compared to the exact solution, the non-staggered grid scheme with higher-order accuracy was found to yield an accuracy significantly better than others. In terms of ‘overall performance’, the so-called 4/1 staggered grid scheme proved to be the best. The simplicity of this scheme is the primary benefit. Furthermore, the scheme can be changed into a non-staggered grid if the pressure is replaced by the pressure gradient as a field variable.Finally, the conventional staggered grid scheme developed by Harlow and Welch also yields relatively high accuracy and demonstrates satisfactory overall performance.

@article{shih1989effects, abstract = {Nine finite difference schemes using primitive variables on various grid arrangements were systematically tested on a benchmark problem of two-dimensional incompressible Navier–Stokes flows. The chosen problem is similar to the classical lid-driven cavity flow, but has a known exact solution. Also, it offers the reader an opportunity to thoroughly evaluate accuracies of various conceptual grid arrangements.Compared to the exact solution, the non-staggered grid scheme with higher-order accuracy was found to yield an accuracy significantly better than others. In terms of ‘overall performance’, the so-called 4/1 staggered grid scheme proved to be the best. The simplicity of this scheme is the primary benefit. Furthermore, the scheme can be changed into a non-staggered grid if the pressure is replaced by the pressure gradient as a field variable.Finally, the conventional staggered grid scheme developed by Harlow and Welch also yields relatively high accuracy and demonstrates satisfactory overall performance.}, added-at = {2015-02-25T22:56:34.000+0100}, author = {Shih, T. M. and Tan, C. H. and Hwang, B. C.}, biburl = {https://www.bibsonomy.org/bibtex/26c6f5c72ca75876ea641482ad9c1d806/aniruddhac}, doi = {10.1002/fld.1650090206}, interhash = {1426dd8eded4aac9e4c7a8d6eff9cb57}, intrahash = {6c6f5c72ca75876ea641482ad9c1d806}, issn = {1097-0363}, journal = {International Journal for Numerical Methods in Fluids}, keywords = {incompressible mms verification}, number = 2, pages = {193--212}, publisher = {John Wiley & Sons, Ltd}, timestamp = {2015-02-25T22:56:34.000+0100}, title = {Effects of grid staggering on numerical schemes}, url = {http://dx.doi.org/10.1002/fld.1650090206}, volume = 9, year = 1989 }