In a cell-centered Finite Volume formulation, the length of cell edges (delta_x and delta_y) are used to calculate the flux. How these lengths are calculated in a vertex-based formulation, especially for an unstructured grid.

Especially consider the case when two vertices have the same x or y coordinate?

Hi If you are looking for info on vertex based unstructured schemes, look for AIAA papers from 88-92 by Tim Barth. He was the pioneer of these methods. Very clearly written papers. Srini

You can go further back, to work at Los Alamos in the early 70's. Their ALE methods were based on vertex-cell ideas.

Look for ALE methods in JCP. In the early to mid-70's, look for YACQUI. Around 1980, look for SALE, CONCHAS, and finally KIVA. Investigators - Hirt, Cloutman, Ruppel, Amsden, Ramshaw - and probably some others.

Check the LANL web sites for open literature reports as well. The reports have especially detailed descriptions of differencing schemes, etc.