On the principal axes of diffusion in difference schemes for 2d transport problems

Via Taylor series, we associate with a difference stencil L^h approximating Lu := au_x + bu_y its modified equation:

Full-size image (1K)

. By rotating axes to eliminate the 2Bu_xy term, the principle axes through which the diffusion in L^h acts is calculated. Interestingly, for many schemes proposed for 2D transport problems these axes have little to do with the “streamline” and ”crosswind” directions of the continuous problem. Several examples are considered from this point of view.