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. T...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 temporal 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 both the mountain-induced Rossby wave and Rossby–Haurwitz wave confirms the appropriate installation of the 3D Coriolis terms in the semi-implicit semi-Lagrangian dynamic core on the Yin-Yang grid.展开更多
With an increase in model resolution,compact high-order numerical advection scheme can improve its effectiveness and competitiveness in oceanic modeling due to its high accuracy and scalability on massive-processor co...With an increase in model resolution,compact high-order numerical advection scheme can improve its effectiveness and competitiveness in oceanic modeling due to its high accuracy and scalability on massive-processor computers.To provide high-quality numerical ocean simulation on overset grids,we tried a novel formulation of the fourth-order multi-moment constrained finite volume scheme to simulate continuous and discontinuous problems in the Cartesian coordinate.Utilizing some degrees of freedom over each cell and derivatives at the cell center,we obtained a two-dimensional(2D)cubic polynomial from which point values on the extended overlap can achieve fourth-order accuracy.However,this interpolation causes a lack of conservation because the flux between the regions are no longer equal;thus,a flux correction is implemented to ensure conservation.A couple of numerical experiments are presented to evaluate the numerical scheme,which confirms its approximately fourth-order accuracy in conservative transportation on overset grid.The test cases reveal that the scheme is effective to suppress numerical oscillation in discontinuous problems,which may be powerful for salinity advection computing with a sharp gradient.展开更多
基金supported by the National Natural Science Foundation of China (Grant No. 41175095)the National Key Technology R&D Program(Grant No. 2012BAC22B01)a research project of the Chinese Academy of Meteorological Sciences (Grant No. 2014Z001)
文摘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 temporal 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 both the mountain-induced Rossby wave and Rossby–Haurwitz wave confirms the appropriate installation of the 3D Coriolis terms in the semi-implicit semi-Lagrangian dynamic core on the Yin-Yang grid.
基金Dr.X.L.Li at the China Meteorological Administration.This study was supported by grants from the National Natural Science Foundation of China(Nos.41575103 and 91637210).
文摘With an increase in model resolution,compact high-order numerical advection scheme can improve its effectiveness and competitiveness in oceanic modeling due to its high accuracy and scalability on massive-processor computers.To provide high-quality numerical ocean simulation on overset grids,we tried a novel formulation of the fourth-order multi-moment constrained finite volume scheme to simulate continuous and discontinuous problems in the Cartesian coordinate.Utilizing some degrees of freedom over each cell and derivatives at the cell center,we obtained a two-dimensional(2D)cubic polynomial from which point values on the extended overlap can achieve fourth-order accuracy.However,this interpolation causes a lack of conservation because the flux between the regions are no longer equal;thus,a flux correction is implemented to ensure conservation.A couple of numerical experiments are presented to evaluate the numerical scheme,which confirms its approximately fourth-order accuracy in conservative transportation on overset grid.The test cases reveal that the scheme is effective to suppress numerical oscillation in discontinuous problems,which may be powerful for salinity advection computing with a sharp gradient.
