Computational grids can play a crucial role in accurate CFD (computational fluid dynamics) simulations. This is shown here through the example of leading-edge vortex flow. Conventional grids for flow over sharp-edged delta wings do not resolve the near-apex flow due to dissimilar length scales of the flow and the grid. This in turn can affect the simulation of many vortex related phenomena. A grid that is consistent with the special nature of the flow is required to overcome the difficulty. The Euler simulation of a transonic vortex is considered where employment of a flow-consistent grid is shown to give a well-resolved vortex with cross-flow shock and also the shock-induced secondary vortex, right from the apex. On the other hand, when a conventional grid is employed these features are absent in the near-apex flow, and the subsequent flow development is seriously affected. Euler simulation of subsonic vortex breakdown has also been considered. In this case the employment of a flow-consistent grid has led to an unravelling of the fine details of the breakdown process.