Lid-driven cavity ﬂows have been widely investigated and accurate results have been achieved as benchmarks for testing the accuracy of computational methods. This paper veriﬁes the accuracy of an adaptive mesh reﬁnement method numerically using 2-D steady incompressible lid-driven ﬂows and coarser meshes. The accuracy is shown by verifying that the centres of vortices given in the benchmarks are located in the reﬁned grids of reﬁned meshes for Reynolds numbers 1000 and 2500 using mesh size 65×65 and 85×85, respectively. The adaptive mesh reﬁnement method performs mesh reﬁnement based on the numerical solutions of Navier-Stokes equations solved by a ﬁnite volume method with well known SIMPLE algorithm for pressure-velocity coupling. The accuracy of the numerical solutions is shown by comparing the proﬁles of horizontal and vertical components of velocity ﬁelds with the corresponding components of the benchmarks together and the streamlines. The adaptive mesh reﬁnement method veriﬁed in this paper can be applied to ﬁnd the accurate numerical solutions of any mathematical models containing continuity equations for incompressible ﬂuid or steady state ﬂuid ﬂows.
|Title of host publication||Proceedings of the 14th International Conference on Computational and Mathematical Methods in Science and Engineering|
|Number of pages||11|
|Publication status||Published - 2014|
|Event||14th International Conference on Computational and Mathematical Methods in Science and Engineering (CMMSE 2014) - Cádiz, Spain|
Duration: 02 Jul 2014 → 06 Jul 2014
|Conference||14th International Conference on Computational and Mathematical Methods in Science and Engineering (CMMSE 2014)|
|Period||02/07/14 → 06/07/14|