On contour crossings in contour-advective simulations – part 1 – algorithm for detection and quantification

This is the first of two papers devoted to the analysis of contour crossing errors that occur in contour-advective simulations of fluid motion. Here an algorithm is presented for quantifying the error due to contour crossings. The first step is to determine the relative proximity of all possible pairs of contours. A digital representation of each contour is produced to aid in the corresponding calculation. Simple analysis of functions is then used to find any crossings between contours deemed close to each other by the digital representation method. Next, the area in error of a pair of crossing contours is calculated by identifying the polygon or polygons that approximately bound the erroneous region. Finally, some preliminary results of analysis of contour crossings that occur in contour-advective semi-lagrangian (CASL) simulations of single layer quasigeostrophic turbulence are presented. It is shown that the error due to contour crossings is small in the simulations considered here.