On spurious behavior of CFD simulations

Spurious behavior in underresolved grids and/or semi-implicit temporal disc retizations for four computational fluid dynamics (CFD) simulations are stu died. The numerical simulations consist of (a) a 1-D chemically relaxed non -equilibrium flow model, (b) the direct numerical simulation (DNS) of 2D in compressible flow over a backward facing step, (c) a loosely coupled approa ch for a 2D fluid-structure interaction, and (d) a 3D unsteady compressible flow simulation of vortex breakdown on delta wings. These examples were ch osen based on their non-apparent spurious behaviors that were difficult to detect without extensive grid and/or temporal refinement studies and withou t some knowledge from dynamical systems theory. Studies revealed the variou s possible dangers of misinterpreting numerical simulation of realistic com plex flows that are constrained by available computing power. In large scal e computations, underresolved grids, semi-implicit procedures, loosely coup led implicit procedures, and insufficiently long-time integration in DNS ar e most often unavoidable. Consequently, care must be taken in both computat ion and in interpretation of the numerical data. The results presented conf irm the important role that dynamical systems theory can play in the unders tanding of the non-linear behavior of numerical algorithms and in aiding th e identification of the sources of numerical uncertainties in CFD. Copyrigh t (C) 1999 John Wiley & Sons, Ltd.