The Problem With Oscillatory Behavior in Grid Convergence Studies

The possibility of oscillatory behavior of the value of a computed variable as grid size is refined in a simulation raises questions in the interpretation of grid convergence studies that have, to the authors' knowledge, never been addressed. Such oscillatory behavior has been observed by the authors, for example, in variables such as wave profiles along the hull and wave elevations in the stern flow in simulations of flows about ships with complex geometries. Roache, in his comprehensive presentation and critique of work up to that time in the area of verification and validation of simulations, points out that 'behavior far away from asymptotic convergence can be non-monotone' and 'the additional assumption of monotone truncation error convergence in the mesh spacing may not be valid for coarse grids, or possibly other conditions'.