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

This is a Preprint and has not been peer reviewed. This is version 2 of this Preprint.

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Authors

Genilson Schunck de Lima, Pedro da Silva Peixoto

Abstract

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.

DOI

https://doi.org/10.31223/X5R04R

Subjects

Numerical Analysis and Computation

Keywords

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

Dates

Published: 2022-03-25 22:19

Last Updated: 2022-03-29 19:33

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License

CC BY Attribution 4.0 International

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