Generalized Z-Grid Model for Numerical Weather Prediction

Atmosphere

Yuanfu Xie¹ 

[1] State Key Laboratory of Severe Weather, Chinese Academy of Meteorological Sciences, China Meteorological Administration, Beijing 100081, China;

关键词: finite volume;    C-grid;    Z-grid;    stability;    numerical efficiency;    shallow water equations;   

DOI  :  10.3390/atmos10040179

来源: DOAJ

【 摘 要 】

Z-grid finite volume models conserve all-scalar quantities as well as energy and potential enstrophy and yield better dispersion relations for shallow water equations than other finite volume models, such as C-grid and C-D grid models; however, they are more expensive to implement. During each time integration, a Z-grid model must solve Poisson equations to convert its vorticity and divergence to a stream function and velocity potential, respectively. To optimally utilize these conversions, we propose a model in which the stability and possibly accuracy on the sphere are improved by introducing more stencils, such that a generalized Z-grid model can utilize longer time-integration steps and reduce computing time. Further, we analyzed the proposed model’s dispersion relation and compared it to that of the original Z-grid model for a linearly rotating shallow water equation, an important property for numerical models solving primitive equations. The analysis results suggest a means of balancing stability and dispersion. Our numerical results also show that the proposed Z-grid model for a shallow water equation is more stable and efficient than the original Z-grid model, increasing the time steps by more than 1.4 times.

【 授权许可】

Unknown