Indented plate problem revisited

An interactive boundary layer method, together with the en approach to the calculation of transition, has been used to investigate the flow over an indented surface for which previous calculations had led to numerical instabilities. The results show two possible reasons for these numerical difficulties. First, it is shown that the gradients of wall shear become very steep at larger Reynolds numbers, particularly in the vicinity of reattachment. Extremely fine numerical grids are required to resolve these gradients. Secondly, and perhaps of greater importance, transition is shown to occur within the region of recirculation for all Reynolds numbers except for the lowest ones. Thus, the calculated flows downstream of the transition locations are fictitious and may be expected to deviate from the corresponding real flows by increasing amounts as the Reynolds number becomes larger. Calculations involving laminar, transitional and turbulent flow have been performed and confirm this conjecture.