A consistent mass-conserving C-staggered method for shallow water equations on global reduced grids

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Genilson Schunck de Lima, Pedro da Silva Peixoto


The increasing number of cores in modern supercomputers motivated the search for methods with better scalability to model the atmospheric dynamics in global weather forecasting and climate simulations. This objective renewed the interest in grid-point schemes with quasi-uniform spherical grids, with each alternative providing some good properties and some disadvantages. Here, we target reduced latitude-longitude global grids, and build from derivations of previous schemes trying to circumvent existing limitations. A method is proposed for the shallow water equations on a C-staggered global reduced grid using a combination of finite differences, finite volumes, and explicit time-stepping. This scheme applies trigonometric approximations, has some conservative properties, and uses numerically consistent operators everywhere. Classical and recently proposed benchmarks were used to evaluate convergence, stability, and accumulation of errors. Results indicated that the trigonometric scheme is a good candidate for global models, providing adequate accuracy at reasonable computational cost and suitability for parallel processing.




Numerical Analysis and Computation


global reduced grids, finite differences, finite volumes, shallow-water equations, conservation, consistency


Published: 2022-03-25 22:19

Last Updated: 2022-03-29 19:33

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CC BY Attribution 4.0 International

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