ON THE RESOLUTION OF CRITICAL FLOW REGIONS IN INVISCID LINEAR AND NONLINEAR INSTABILITY CALCULATIONS

Numerical methods for tackling the inviscid instability problem are di scussed. Convergence is demonstrated to be a necessary, but not a suff icient condition for accuracy. Inviscid flow physics set requirements regarding grid-point distribution in order for physically accurate res ults to be obtained. These requirements are relevant to the viscous pr oblem also and are shown to be related to the resolution of the critic al layers. In this respect, high-resolution nonlinear calculations bas ed on the inviscid initial-boundary-value problem are presented for a model shear-layer flow, aiming at identification of the regions that r equire attention in the course of high-Reynolds-number viscous calcula tions. The results bear a remarkable resemblance with those pertinent to viscous flow, with a cascade of high-shear regions being shed towar ds the vortex-core centre as time progresses. In parallel, numerical i nstability related to the finite-time singularity of the nonlinear equ ations solved globally contaminates and eventually destroys the simula tions, irrespective of resolution.