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.
%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
}