1. A Verification Suite of Test Cases for the Barotropic Solver of Ocean Models.
- Author
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Bishnu, Siddhartha, Petersen, Mark R., Quaife, Bryan, and Schoonover, Joseph
- Subjects
SPECTRAL element method ,FINITE volume method ,OCEAN waves ,ROSSBY waves ,ATMOSPHERIC models ,CYCLOGENESIS ,OCEAN ,WATER depth ,ATMOSPHERE - Abstract
The development of any atmosphere or ocean model warrants a suite of test cases (TCs) to verify its spatial and temporal discretizations, order of accuracy, stability, reproducibility, portability, scalability, etc. In this paper, we present a suite of shallow water TCs 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 TCs 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. The experimental procedure for conducting these numerical experiments is detailed. It underscores several key considerations that vary depending on the chosen spatial discretization method. Finally, convergence studies of every TC are conducted with refinement in both space and time, only in space, and only in time. The convergence slopes match the expected theoretical predictions. Plain Language Summary: Before running an atmosphere, ocean, or a coupled climate simulation, every model developer should ensure the correct implementation of each term in the governing equations that drive the models forward in time. This motivates the development of idealized test cases (TCs), each of which verifies a subset of terms in the governing equations with different initial and boundary conditions. Here we present a suite of six TCs for the momentum equation and sea surface height equation for ocean models in a single‐layer configuration. The computed results from the ocean model can be compared to exact solutions. The computed solution always has a small error, but is said to converge to the exact solution with reduction in grid cell size and time step. If the model converges at the expected rate, then we know that it is solving the governing equations correctly. We show results of convergence tests from two models, and share the full specifications of these TCs so that other ocean modelers may reproduce them. Key Points: A suite of test cases is presented for the verification of barotropic dynamics of ocean models, with exact and manufactured solutionsSpecifications are provided for coastal Kelvin wave, inertia‐gravity wave, planetary and topographic Rossby waves, barotropic tide, and non‐linear casesResults are presented for a variety of time‐stepping methods and two types of spatial discretizations: TRiSK and discontinuous Galerkin spectral element method [ABSTRACT FROM AUTHOR]
- Published
- 2024
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