NUMERICS AND HYDRODYNAMIC STABILITY - TOWARD ERROR CONTROL IN COMPUTATIONAL FLUID-DYNAMICS

We critically review the available error analysis in computational flu id dynamics (CFD) and come to the conclusion that the existing error e stimates are meaningless in most cases of interest. We propose a new a pproach to error analysis in CFD aiming at reliable and efficient adap tive quantitative error control. This is based on a precise analysis o f hydrodynamic stability coupled with Galerkin orthogonality. We prove a priori- and a posteriori-type error estimates in a model case for p ipe flow, formulate corresponding adaptive algorithms, and discuss the potential of this approach for adaptive error control in CFD.