An Improved Dynamic Core Of The GRAPES On The Yin-yang Grid

A 3D dynamic core of the non-hydrostatic model GRAPES(Global/Regional Assimilation and Prediction System) is developed on the Yin-Yang grid to address the polar problem and to enhance the computational efficiency. Three-dimensional Coriolis forcing is introduced to the new core, and full representation of the Coriolis forcing makes it straightforward to share code between the Yin and Yang subdomains. Similar to that in the original GRAPES model, a semi-implicit semi-Lagrangian scheme is adopted for tempora l integration and advection with additional arrangement for cross-boundary transport. Under a non-centered second-order temporal and spatial discretization, the dry nonhydrostatic frame is summarized as the solution of an elliptical problem. The resulting Helmholtz equation is solved with the Generalized Conjugate Residual solver in cooperation with the classic Schwarz method. Even though the coefficients of the equation are quite different from those in the original model, the computational procedure of the new core is just the same. The bi-cubic Lagrangian interpolation serves to provide Dirichlet-type boundary conditions with data transfer between the subdomains. The dry core is evaluated with several benchmark test cases, and all the tests display reasonable numerical stability and computing performance. Persistency of the balanced flow and development of all the mountain-induced Rossby wave, baroclinic wave and Rossby–Haurwitz wave confirms the appropriate installation of the 3D Coriolis terms in the sem i-implicit semi-Lagrangian dynamic core on the Yin-Yang grid. The piecewise rational method(PRM) is choosed as the advection transport scheme for water vapor. Even though the existence of the inner boundary on the Yin-Yang grid, its advantages such as convexity preserving nature, numerical accuracy and shape-preserving property can be drawn for the numerical result of the advection of solid body test.