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《Chinese Journal of Atmospheric Sciences》 2006-01
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On the Time Step of Semi-Lagrangian Semi-Implicit Atmospheric Model

HU Zhi-Jin and SHI Yue-QinChinese Academy of Meteorological Sciences,Beijing 100081  
Semi-Lagrangian Semi-Implicit(SLSI) atmospheric model has some advantages and a longer time step is usually used.The limitation of the time step for SLSI model is discussed.The source-sink term in SLSI model is usually calculated by the average value at departure and arrived time-space points.Serious computation error is shown in a stationary point source case with a constant advection speed u_(0) by using a usual SLSI model if time step Δt is significantly greater than ΔX/u_(0),where Δt is time step and ΔX is grid spacing.These errors could not be reduced by using the weighted average value of the source-sink term.It is shown in this simple case that the accurate results can be gotten if an accurate form of the source-sink term is used.To ensure the accuracy of SLSI model for calculating the nonliner source-sink term case there is the alternative of the simplified scheme with a shorter time step or the sophisticated scheme with a longer time step.Atmospheric waves also have a nonliner source-sink term.It is shown in a non-advection wave case that the absolute value of source term by using the averaged value at beginning and end points is always less than the accurate ones.The computation error grows with Δt,and becomes serious for ΔtT_w/4,where T_w is time period of the wave.The solution becomes a stationary one when Δt=T_w/2.Better results are given by using the sophisticated source scheme for ΔtT_w/4.But significant error appears when ΔtT_w/4,and simulated wave becomes a standing one for Δt=T_w/2.Generally speaking,minimum period and length(T_(min),L_(min)) of atmospheric waves,which may be simulated by the model,are determined by the time step and grid length(Δt,ΔX),such as T_(min)=4Δt,L_(min)=4ΔX.Serious error occurring in calculating the shorter wave(T4Δt) is inevitable as shown in the above case.T_(min) will match with L_(min) when Δt=ΔX/C_0,where C_(0) is the wave speed.If ΔtΔX/C_0,only waves with L4Δt·C_0 can be accurately simulated by the model,but waves with 4ΔXL4Δt·C_0 will be misrepresented.So the Courant number N_C=C·Δt/ΔX is a useful index for determining the Δt value in all atmospheric models.Various atmospheric phenomena have different typical life time(T_(a)) and size(L_(a)).Δt T_(a) /4 and ΔX L_(a) /4 are essential for correct simulation.The SLSI model has better computation stability even if a longer time step Δt is used.But the characteristic time(T_(0)) of cloud or atmospheric chemical processes must be considered in calculating the positively defined variables.The calculated value may be negative when ΔtT_0 for explicit model or Δt2T_0 for the SLSI model,which leads to an unreasonable result.
【Fund】: 国家重点基础研究发展规划项目G1998040912、2004CB418306;; 国家自然科学基金资助项目40305001
【CateGory Index】: P435
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【Citations】
Chinese Journal Full-text Database 2 Hits
1 Chen Jiabin (Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing l00029) Ji Zhongzhen (State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics, Institute of Atmospheric Physics, Chinese Academy;A Study of Energy-Conserving Semi-Lagrangian Scheme[J];Chinese Journal of Atmospheric Sciences;2001-06
2 Chen Jiabin 1) , and Ji Zhongzhen 2) 1) (Institute of Atmospheric Physics,Chinese Academy of Sciences, Beijing 100029) 2) (State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029);A Study of Complete Square-Conserving Semi-Implicit Semi-Lagrangian Scheme[J];Chinese Journal of Atmospheric Sciences;2004-04
【Co-citations】
Chinese Journal Full-text Database 10 Hits
1 Mu Mu, Ji Zhongzhen, Wang Bin, and Li Yang (Institute of Atmospheric Physics , Chinese Academy of Sciences , Beijing 100029);Achievements in Geophysical Fluid Dynamics[J];Chinese Journal of Atmospheric Sciences;2003-04
2 Lin Wantao, and Xie Zhenghui(State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029);The Computational Stability of Nonconservative Schemes of Nonlinear Evolution Equations[J];Chinese Journal of Atmospheric Sciences;2004-04
3 Chen Jiabin 1) , and Ji Zhongzhen 2) 1) (Institute of Atmospheric Physics,Chinese Academy of Sciences, Beijing 100029) 2) (State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029);A Study of Complete Square-Conserving Semi-Implicit Semi-Lagrangian Scheme[J];Chinese Journal of Atmospheric Sciences;2004-04
4 JI Li-Ren 1, 2, CHEN Jia-Bin1, ZHANG Dao-Min1, and WANG Hou-Jun3 1Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029 2State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029 3University of Maryland, Maryland, USA;Review of Some Numerical Aspects of the Dynamic Framework of NWP Model[J];Chinese Journal of Atmospheric Sciences;2005-01
5 YANG XueSheng1,CHEN JiaBin2,HU JiangLin1,CHEN DeHui1,SHEN XueShun1,ZHANG HongLiang1 1 State Key Laboratory of Severe Weather,Chinese Academy of Meteorological Sciences,Beijing 100081,China;2 State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics,Institute of Atmospheric Physics,Beijing 100029,China;A semi-implicit semi-Lagrangian global nonhydrostatic model and the polar discretization scheme[J];中国科学(D辑:地球科学)(英文版);2007-12
6 LUO Li,FENG Jian-hu ( College of Science,Chang′an University,Xi′an 710064,China);Characteristic-based Central FVM for Burgers Equation[J];Aeronautical Computing Technique;2010-03
7 DU Hua-dong,HUANG Si-xun,SHI Han-qing(The College of Meteorology of the Institute of Science and Engineering of the P.L.A, Nanjing 211101, China);Theoretical analysis and numerical experiment for 1-D semi-geostrophic shallow water model[J];Journal of Hydrodynamics;2004-01
8 CAO Xiao-qun, HUANG Si-xun, DU Hua-dong ( Institute of Meteorology, PLA Unvi. of Sci. & Tech. , Nanjing 211101,China; Jiangsu Province Key Laboratory of Meteorlogical Disaster and Environmental Variation, Nanjing 210044 ,China);Theoretical analysis and numerical experiments of single-Doppler wind retrieval[J];Journal of Hydrodynamics;2005-03
9 ZHOU Cheng- jun1,GENG Liang- guo2, LI Jun- wei2 (1.The Institute of Meteorology of the PLA University of Science and Technolo gy,Nanjing 211101,China, 2.The Observatory of the Air Force 93318 Unit, Kaiyuan 112300,China);The Optimal Method of the Initial Data in the Precipitation Forecast[J];Bimonthly of Xinjiang Meteorology;2005-03
10 Chen Fengfeng Wang Guanghui Shen Xueshun Chen Dehui Hu Jianglin(State Key Laboratory of Severe Weather,Chinese Academy of Meteorological Sciences,Beijing 100081);Application of Cascade Interpolation to GRAPES Model[J];Journal of Applied Meteorological Science;2009-02
【Secondary Citations】
Chinese Journal Full-text Database 2 Hits
1 Ji Zhpngzhen and Wang Bin(LASG , Institute of Atmospheric Physics, Chinese Academy of Sciences);FURTHER DISCUSSION ON THE CONSTRUCTION AND APPLICATION OF DIFFERENCE SCHEME OF EVOLUTION EQUATIONS[J];Chinese Journal of Atmospheric Sciences;1991-02
2 Chen Jiabin (Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing l00029) Ji Zhongzhen (State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics, Institute of Atmospheric Physics, Chinese Academy;A Study of Energy-Conserving Semi-Lagrangian Scheme[J];Chinese Journal of Atmospheric Sciences;2001-06
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