FVCOM validation experiments: Comparisons with ROMS for three idealized barotropic test problems

The unstructured-grid Finite-Volume Coastal Ocean Model (FVCOM) is evaluated using three idealized benchmark test problems: the Rossby equatorial soliton, the hydraulic jump, and the three-dimensional barotropic wind-driven basin. These test cases examine the properties of numerical dispersion and damping, the performance of the nonlinear advection scheme for supercritical flow conditions, and the accuracy of the implicit vertical viscosity scheme in barotropic settings, respectively. It is demonstrated that FVCOM provides overall a second-order spatial accuracy for the vertically averaged equations (i.e., external mode), and with increasing grid resolution the model-computed solutions show a fast convergence toward the analytic solutions regardless of the particular triangulation method. Examples are provided to illustrate the ability of FVCOM to facilitate local grid refinement and speed up computation. Comparisons are also made between FVCOM and the structured-grid Regional Ocean Modeling System (ROMS) for these test cases. For the linear problem in a simple rectangular domain, i.e., the wind-driven basin case, the performance of the two models is quite similar. For the nonlinear case, such as the Rossby equatorial soliton, the second-order advection scheme used in FVCOM is almost as accurate as the fourth-order advection scheme implemented in ROMS if the horizontal resolution is relatively high. FVCOM has taken advantage of the new development in computational fluid dynamics in resolving flow problems containing discontinuities. One salient feature illustrated by the three-dimensional barotropic wind-driven basin case is that FVCOM and ROMS simulations show different responses to the refinement of grid size in the horizontal and in the vertical.