It is difficult to know a priori whether or not a flow solver works well on a generated grid system. In the study of grid generation, this has become bottle-neck of progress. This paper describes an effect of grid quality on the accuracy and convergency of computations. Firstly, simple model equations with a characteristic feature of the Navier-Stokes equations are introduced. Secondly, a simple diagnosis for the quality of the grid systems is focused on. Finally, an adaptive gridding technique is proposed as a prescription, in which errors estimated by the simple model equations are regarded as a weighting function.