Development of high-order adaptive global models by multi-moment (constrained) finite volume method
Seminar Room 1, Newton Institute
The numerical schemes using multi-moment concepts were developed recently. More than one kinds of moments, which denote the discrete quantities of the physical fields from different aspects, such as point value (PV), volume-integrated average (VIA), derivative values (DVs) of different orders and so on, are adopted as model variables or constraints to build high-order schemes with local (usually single-cell based) reconstructions. The concise formulations are derived to update different moments. The numerical conservation is always preserved through updating VIA by flux-form formulation. Compared to other advanced methods with local reconstruction, the multi-moment schemes often allow the larger CFL numbers and are more flexible for different applications, and thus are very suited for developing global models for atmospheric and oceanic dynamics. This talk will mainly report the following progress we have recently made to develop global models using multi-moment method. 1) A global SWE model up to fifth-order accuracy has been developed on cubed sphere. Compact reconstruction stencil is beneficial to reducing the excessive errors due to the discontinuous coordinates on adjacent patches. Furthermore, the AMR technique has be extended to spherical geometry on cubed sphere using a multi-moment finite volume formulation. 2) Multi-moment schemes have been used to construct high-order numerical models on icosahedral grid, which is a kind of unstructured grid in nature. By defining 7 and 10 DOFs within each element, the third- and fourth-order global SWE models have been developed on triangular- and hexagonal-type tessellations. 3) Two-dimensional non-hydrostatic model has been developed using the third- and fourth-order multi-moment constrained schemes. Proposed models have been checked by benchmark tests and the results are competitive to most existing models. The multi-moment framework is very promising for developing the high-performance dynamic core for GCMs.