Accuracy analysis of an adaptive mesh refinement method using benchmarks of 2-D steady incompressible lid-driven cavity flows

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.