An adaptive nonhydrostatic dynamical core using a multimoment finite‐volume method on a cubed sphere

Abstract

Abstract: An adaptive nonhydrostatic atmospheric dynamical core was developed on a Cartesian grid and extended to spherical geometry with the application of a cubed‐sphere grid. To assure a practical Courant‐Friedrichs‐Lewy number for stability, a horizontally explicit and vertically implicit algorithm was applied in this model through a third‐order implicit–explicit Runge–Kutta scheme. A two‐dimensional adaptive grid was applied in the horizontal directions to generate the computational meshes, with variable resolutions according to the evolution of the predicted variables during the simulations, while the vertical grid is fixed considering the characteristics of atmospheric flows and the computational efficiency in practical applications. The Berger–Oliger block‐structured adaptive algorithm was adopted in this study. Blocks with different resolutions can be constructed straightforwardly on each patch of the cubed sphere and an algorithm to exchange both solution and block information between adjacent patches was designed in order to implement a global model. The nonhydrostatic governing equations are solved by a three‐point multimoment constrained finite‐volume scheme. Using the compact stencil for spatial reconstructions, the interpolation operations between coarse–fine blocks can be implemented efficiently and the local‐based scheme is also helpful to suppress the computational modes around the coarse–fine interfaces due to the abrupt change of grid resolution. Additionally, flux corrections were conducted along the block boundaries and the resulting dynamical core is rigorously conservative. The proposed model was evaluated by calculating several idealized benchmark tests, and the effectiveness of the adaptive model in saving computational costs was verified in this study.