Use of an HOC scheme to determine the existence of multiple steady states in the antiparallel lid-driven flow in a two-sided square cavity

Though the existence of multiple steady states for the antiparallel lid motion is known only for two-sided rectangular cavity flows, this work demonstrates for the first time that such solutions exist for a square cavity as well if the Reynolds number (Re) exceeds the threshold value of 3202. To obtain accurate results a higher-order compact (HOC) scheme of spatially fourth- and temporally second-order accuracy is used. It is also known that multiple solutions exist at all aspect ratios for the parallel motion in a two-sided cavity above a certain Re value. Earlier computations for parallel and antiparallel lid motion have been carried out using non-compact schemes. In this work much care has been observed to carry out highly accurate computations using the HOC scheme to re-examine these cases as well. Tabulated values of various parameters serve as a means of comparison to determine the accuracy of other solution methods.