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

Abstract

The increasing number of cores in modern supercomputers motivated the search for methods with good scalability to model global problems in geophysical fluid dynamics, including the representation of the atmospheric dynamics in global weather forecasting and climate simulations. Grid-point schemes with quasi-uniform spherical grids, along with explicit time integration, are one of the known options for recent dynamical core developments. These methods avoid the concentration of points in the poles and do not require global communication, intending to contribute to the efficiency of parallel implementations. On the other hand, they may yield low accuracy or present errors stimulated by the grid. Here, we target reduced latitude-longitude global grids and build from derivations of previous schemes to propose a method 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 employs only local 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 proposed scheme provides adequate accuracy at competitive computational cost.