The development of any atmosphere or ocean model warrants a suite of
test cases to verify its spatial and temporal discretizations, order of
accuracy, stability, reproducability, portability, scalability, etc. In
this paper, we present a suite of shallow water test cases designed to
verify the barotropic solver of atmosphere and ocean models. These
include the non-dispersive coastal Kelvin wave; the dispersive
inertia-gravity wave; the dispersive planetary and topographic Rossby
waves; the barotropic tide; and a non-linear manufactured solution.
These test cases check the implementation of the linear pressure
gradient term; the linear constant or variable-coefficient Coriolis and
bathymetry terms; and the non-linear advection terms. Simulation results
are presented for a variety of time-stepping methods as well as two
spatial discretizations: a mimetic finite volume method based on the
TRiSK scheme, and a high-order discontinuous Galerkin spectral element
method. We explain the strategies that need to be adopted for specifying
initial and non-periodic boundary conditions on hexagonal meshes.
Convergence studies of every test case are conducted with refinement in
both space and time, only in space, and only in time. The convergence
slopes match the expected theoretical predictions.