On the Relationship between Mesh Refinement and Solution Accuracy

The ability to identify and quantify the various sources of error in a CFD computation is an essential requirement if numerical simulation is to be applied with confidence to aerodynamic design. Lack of adequate mesh resolution is just one of the many sources of error but it is a concern that invariably arises whenever a discretized set of equations is solved by a finite element or finite volume method. This paper attempts to formalize some of the notions of how solution error is related to mesh size and to derive conditions that determine whether Richardson extrapolation can be applied. In particular, it is shown that Richardson extrapolation can be used to assess convergence with respect to mesh size provided the candidate meshes are fine enough to be in the asymptotic range. It is also shown that non-uniform refinement of the mesh will usually lead to an exponent of error reduction that diers from the formal accuracy of the discretized equations.