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Feng Xiao

2012-11-06
15:40:00 - 17:00:00

308 , Mathematics Research Center Building (ori. New Math. Bldg.)

Simultaneously using multiple discrete moments of a physical field, like cell integrated average, point value and derivatives, as the predicted variables or the constraints to derive the evolution equations for the predicted variables provides a new alternative framework to construct high order schemes. High order multi-moment methods have attractive properties for practical applications, such as algorithmic simplicity, flexibility and computational efficiency, hence are expected to be the suitable core numerics for new-generation models of global atmospheric and oceanic circulations. This talk will present some of our recent efforts toward the establishment of a new numerical model for atmospheric global circulations, using high-order multi-moment constrained finite volume (MCV) method. 1) In order to circumvent the polar problems in the conventional latitude-longitude grid, global shallow water models have been developed for spherical geometry on several popular spherical grids that have uniform grid spacing, including Yin-Yang composite grid, cubed sphere grid, icosahedral geodesic grid with both triangular and hexagonal tessellations. Widely used benchmark test problems were used to evaluate the numerical models, which verifies that the proposed numerical formulation works very well for different kinds of spherical grids and is promising for developing high-performance dynamic cores for global models. 2) Non-hydrostatic compressible dynamic core for atmosphere has been also developed by using the 3rd and 4th order MCV schemes. Two important features make MCV method particularly attractive as an accurate and practical numerical framework for atmospheric modelling. 1) Using nodal values as the predicted variables at solution points that can be flexibly located within the computational domain provides a great convenience in dealing with complex geometry and source terms including those from physical packages, and 2) High order schemes can be built by using constraints in terms of different moments, which makes the numerical model more robust and efficient (stable for larger CFL number). Numerical tests including the topographic effects have been conducted to evaluate the non-hydrostatic dynamic core as an accurate and practical framework for atmospheric models.