A comparative study of explicit differential operators on arbitrary grids

We compare explicit differential operators for unstructured grids and their accuracy with the aim of solving time-dependent partial differential equat ions in geophysical applications. As many problems suggest the use of stagg ered grids we investigate different schemes for the calculation of space de rivatives on two separate grids. The differential operators are explicit an d local in the sense that they use only information of the function in thei r nearest neighborhood, so that no matrix inversion is necessary. This make s this approach well-suited for parallelization. Differential weights axe o btained either with the finite-volume method or using natural neighbor coor dinates. Unstructured grids have advantages concerning the simulation of co mplex geometries and boundaries. Our results show that while in general tri angular (hexagonal) grids perform worse than standard finite-difference app roaches, the effects of grid irregularities on the accuracy of the space de rivatives are comparably small for realistic grids. This suggests that such a finite-difference-like approach to unstructured grids may be an alternat ive to other irregular grid methods such as the finite-element technique.