Review on development of a scalable high-order nonhydrostatic multi-moment constrained finite volume dynamical core.

This report summarizes the major progresses to develop the dynamic core for next-generation atmospherical model for both numerical weather prediction and climate simulation. The numerical framework is based on a general formulation, so-called multi-moment constrained finite volume (MCV) method, which is well-balanced among solution quality (accuracy and robustness), algorithmic simplicity, computational efficiency and flexibility for model configuration. A local high-order limiting projection is also devised to remove spurious oscillations and noises in numerical solutions, which allows the numerical model working well alone without artificial diffusion or filter. The resulted numerical schemes are very simple, efficient and easy to implement for both structured and unstructured grids, which provide a promising plateform of great practical significance. We have implemented the MCV method to shallow water equations on various spherical grids, including Yin-Yang overset grid, cubed sphere grid and geodesic icosahedral grid, non-hydrostatic compressible atmosherical model under complex topographic boundary conditions. In addition, the moist dynamics simulation like moist thermal bubble has been validated by using direct microphysical feedback. We have also constructed a prototype of 3D global non-hydrostatic compressible atmosherical model on cubed sphere grid with an explicit/implicit-hybrid time integration scheme, which can be used as the base to develop global atmospheric GCM. All the MCV models have been verified with widely used benchmark tests. The numerical results show that the present MCV models have solution quality competitive to other exiting high order models. Parallelization of the MCV shallow water model on cubed sphere grid reveals its suitability for large scale parallel processing with desirable scalability.