Staggered grids for multidimensional multiscale modelling

The paper establishes the stability/accuracy classification and counts entirely via large-scale numerical eigenanalysis, reporting that only grids whose four patches are all symmetric are stable (1,248 of 167,040), and that only the 120 centred grids are both stable and accurate; it provides no analytic proof, explicitly noting symbolic attempts failed and resorting to numerical computation of the one-cell Jacobian spectrum . By contrast, the model gives principled proof sketches: (i) a discrete SBP energy argument showing pairwise flux cancellation and nonpositive symmetric part of the Jacobian for symmetric patches (hence stability), and (ii) an exact plane-wave eigenvector argument for centred grids plus a cos(κ/2) symbol defect for non-centred grids (hence inaccuracy). These sketches align with the paper’s definitions (spectral coupling with two normal edge layers; macroscale accuracy judged against the full-domain staggered discretization eigenvalues (10) ) and reproduce the paper’s counts. Because the paper does not supply proofs while the model provides coherent analytic reasoning that matches the reported phenomena and counts, the appropriate audit verdict is that the paper is incomplete while the model is correct.