A Positivity-preserving Conservative Semi-Lagrangian Multi-moment Global Transport Model on the Cubed Sphere  

作　　者：Jie TANG Chungang CHEN Xueshun SHEN Feng XIAO Xingliang LI 

机构地区：[1]National Meteorological Center/Center of Numerical Weather Predication,China Meteorological Administration,Beijing 100081,China [2]State Key Laboratory for Strength and Vibration of Mechanical Structures&School of Aerospace Engineering,Xi’an Jiaotong University,Xi’an 710049,China [3]Department of Mechanical Engineering,Tokyo Institute of Technology,Tokyo 152-8850,Japan

出　　处：《Advances in Atmospheric Sciences》2021年第9期1460-1473,共14页大气科学进展（英文版）

基　　金：supported by the National Key Research and Development Program of China (Grant Nos.2017YFC1501901 and 2017YFA0603901);the Beijing Natural Science Foundation (Grant No.JQ18001)。

摘　　要：A positivity-preserving conservative semi-Lagrangian transport model by multi-moment finite volume method has been developed on the cubed-sphere grid.Two kinds of moments(i.e.,point values(PV moment) at cell interfaces and volume integrated average(VIA moment) value) are defined within a single cell.The PV moment is updated by a conventional semi-Lagrangian method,while the VIA moment is cast by the flux form formulation to assure the exact numerical conservation.Different from the spatial approximation used in the CSL2(conservative semi-Lagrangian scheme with second order polynomial function) scheme,a monotonic rational function which can effectively remove non-physical oscillations is reconstructed within a single cell by the PV moments and VIA moment.To achieve exactly positive-definite preserving,two kinds of corrections are made on the original conservative semi-Lagrangian with rational function(CSLR)scheme.The resulting scheme is inherently conservative,non-negative,and allows a Courant number larger than one.Moreover,the spatial reconstruction can be performed within a single cell,which is very efficient and economical for practical implementation.In addition,a dimension-splitting approach coupled with multi-moment finite volume scheme is adopted on cubed-sphere geometry,which benefitsthe implementation of the 1 D CSLR solver with large Courant number.The proposed model is evaluated by several widely used benchmark tests on cubed-sphere geometry.Numerical results show that the proposed transport model can effectively remove nonphysical oscillations and preserve the numerical nonnegativity,and it has the potential to transport the tracers accurately in a real atmospheric model.

关 键 词：global transport model cubed-sphere grid multi-moment method single-cell-based scheme conservative semi-Lagrangian method 

分 类 号：P456.7[天文地球—大气科学及气象学]