An unstructured finite volume method for large-scale shallow flows using the fourth-order Adams scheme

In this paper, we introduce a new upwind finite volume method using unstructured grids for large-scale shallow flows. This method uses a high-order upwind scheme for the calculation of the numerical flux, and the fourth-order Adams method with a splitting approach for time integration. The process includes three stages: in the first and third steps the Coriolis term is integrated analytically, and in the second step the flux term is integrated numerically. Most upwind schemes perform well for gravity waves but they lead to a high level of damping or numerical oscillations for Rossby waves. The proposed method presents the advantage that it performs well for both gravity and Rossby waves. The use of fourth-order Adams method without any iteration on the corrector is enough to suppress the short-wave numerical noise without damping the long waves that are essential in the transport of energy Rossby waves, in large-scale oceanic and atmospheric flows.