Nonlinear Interaction of Friction and Interpolation Errors in Unsteady Flow Analyses

Abstract

Explicit analytical assessments of numerical errors in solutions of decaying standing waves in pipes are obtained using analyses based on the fixed-grid method of characteristics and are used as a quantitative basis for comparing alternative grid types, sizes, and shapes. It is shown that the influences of friction and interpolation combine in a nonlinear manner, but that the combination has the form of a product so that the two effects may be considered independently to a certain extent. The analysis is presented for finite pipes, thus creating both upper and lower limits for the range of possible standing wave frequencies. It is found that frequencies in the upper half of the range are strongly damped. The performances of diamond and rectangular grids are compared, but there is no clear winner because, for equivalent computer resources, each has both advantages and disadvantages. The overall purposes of the paper are to move toward methods of (1) relieving untrained software users from tasks related to grid selection and (2) assisting third parties in assessing the validity of numerical results undertaken by others.