Assessing grid quality of structured meshes by truncation error analysis

Abstract

Using Couette flow as an example, it has been shown that analysis of the metric terms of a truncation error equation is an effective method of evaluating the grid quality of a structured mesh. However, there are limitations to analyzing mesh quality in this manner. First, though four grid quality measures are derived, GE ₁ to GE ₄, for the Navier-Stokes equations, only GE ₁ and GE ₂ reflect the error characteristics of the numerical solution. This is due to the nature of the laminar Couette flow: all x-derivatives and second order and higher y-derivatives vanish. For problems more complex than the Couette flow case presented here, all grid quality measures may have to be evaluated. Second, the grid quality measures do not predict the magnitude of the solution error caused by poor grid quality. This is due to the fact that the in addition to the metric terms, the solution itself plays a major role in determining the magnitude of the truncation error. Moreover the magnitude of the truncation error does not correspond to the magnitude of the solution error. What can be said, however, is that the grid quality measures do point out areas in the numerical mesh where grid induced errors may occur. In closing, it should be noted that the Couette flow problem used in this paper is perhaps one of the simplest flow problems to analyze. In further research a more complicated flow problem may be desirable. The exercise performed here has revealed that grid quality analysis involve more complex measures than the traditional grid quality values used in the past.