Effect of grid quality on the accuracy and convergency of computations

摘要

It is difficult to know a priori whether a flow solver works well on a generated grid system. ^In the study of grid generation, this has become a bottleneck for progress. ^This paper describes an effect of grid quality on the accuracy and convergence of computations. ^First, we introduce some simple diagnoses for the quality of a grid system. ^Several simple model equations with a characteristic feature of the Navier-Stokes equations are exploited. ^Second, we attempt to find a weighting function for adaptation. ^In this stage, it is found that a distribution of the source term in the well-known elliptic grid generation systems using Poisson's equation is a key to estimating the quality of the generated grid system and to improving the grid. ^Finally, we propose an adaptive gridding technique as a prescription. ^Errors estimated by a stability analysis of a numerical scheme and simple model equations are regarded as the weighting functions. ^The grid is modified according to those functions. ^As a result, the grid quality is enhanced. ^(Author)