Accuracy verification of a 2D adaptive mesh refinement method by the benchmarks of lid-driven cavity flows with an arbitrary number of refinements

The lid-driven cavity flow problem stands as a widely recognized benchmark in fluid dynamics, serving to validate CFD algorithms. Despite its geometric simplicity, the lid-driven cavity flow problem exhibits a complex flow regime primarily characterized by the formation of vortices at the centre and corners of the square domain. This study evaluates the accuracy of the 2D velocity-driven adaptive mesh refinement (2D VDAMR) method in estimating vortex centres in a steady incompressible flow within a 2D square cavity. The VDAMR algorithm allows for an arbitrary number of finite mesh refinements. Increasing the number of successive mesh refinements results in more accurate outcomes. In this paper, the initial coarse uniform grid mesh was refined ten times for Reynolds numbers (Formula presented.). Results show that VDAMR accurately identifies vortex centres, with its findings closely aligning with benchmark data from six literature sources.