INTERPOLATION IN TRANSIENT POLYTROPIC FLOW

An accurate method of space-line interpolation between known parameter values at discretely spaced points in a numerical grid is introduced. The method-designated 'quasi-steady' or 'physical' interpolation-is c onceptually simple, being based on a physical interpretation of flow. Its greatest value is in spatially varied regions of flow. Potential a pplications include free-surface hows, two-phase flows and general 3D gas flows, but this paper is restricted to the analytically simple cas e of polytropic gas flows. In sufficiently simple steady flows, the pr oposed method is potentially exact. It is used herein to assess the ac curacy of (a) linear interpolation and (b) some cubic interpolation sc hemes related to those discussed by Murray in Ref [1]. The latter are found to be potentially more accurate than the former, but less ''safe ''-special care must be taken to avoid undesirable behaviour at high M ach numbers. No method of interpolating between discrete points can be universally exact. In unsteady flows, for example, an infinity of alt ernatives could be physically possible, particularly when discontinuit ies exist between adjacent grid points. Two proposed implementations o f the quasi-steady method lead to plausible approximations to unsteady flow distributions. It is shown that they will typically be more accu rate than linear or cubic methods. Despite its greater accuracy, the q uasi-steady method should not always be used in preference to other me thods. Alternative criteria as simplicity can also be relevant. (C) 19 98 Elsevier Science Ltd. All rights reserved.