Discussion of "Finite Volume Model for Two-Dimensional Shallow Water Flows on Unstructured Grids" by Tae Hoon Yoon and Seok-Koo Kang

The authors should be congratulated for their interesting paper regarding the numerical model, which is based on a second-order upwind finite volume method on unstructured triangular grids applied to the shallow water equations (SWE). Because of this unstructured grid, complex geometries can be handled with ease. It is clearly an important advantage of the proposed method. However, we would like to draw the reader's attention to a serious problem with discretization of the SWE for arbitrary geometry with a triangular grid, namely, the compatible treatment of the pressure and bed-slope terms. Unfortunately, the authors did not describe how they demonstrated the stability of their method for an arbitrary bed geometry. As described by Nujic (1995), improper treatment of the bottom slope term may lead to inaccuracies; by referring to Komaei (2004) and Farshi (2002), it is important for an unstructured grid, where the method presented in the paper could be neither compatible nor conservative. For water initially at rest, a typical instability form is a movement without physical reason after a few computational cycles. To demonstrate this outcome, consider a triangular cell according to Fig. I and apply the method presented in the paper.