关于半拉格朗日半隐式大气模式的时步问题  

On the Time Step of Semi-Lagrangian Semi-Implicit Atmospheric Model

作　　者：胡志晋[1] 史月琴[1] 

机构地区：[1]中国气象科学研究院,北京100081

出　　处：《大气科学》2006年第1期1-10,共10页Chinese Journal of Atmospheric Sciences

基　　金：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

摘　　要：讨论半拉格朗日半隐式大气模式中时步的限制,展示时步过大时用一般的首尾两点平均方案计算非线性源汇项的严重误差,提出精确的源汇项计算格式并作了特例计算和比较,讨论了被模拟的大气过程和波动的特征对时步的要求,指出柯朗数NC=C.Δt/ΔX是大气模式时空步长匹配的重要参数。指出云降水和大气化学过程特征时间对相应的正定变量的计算时步的限制。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 u0 by using a usual SLSI model if time step At is significantly greater than △X/u0, where At is time step and △X 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 At, and becomes serious for △t〉Tw/4, where Tw is time period of the wave. The solution becomes a stationary one when △t= Tw/2. Better results are given by using the sophisticated source scheme for △t〈Tw/4. But significant error appears when △t〉Tw/4, and simulated wave becomes a standing one for △t=Tw/2. Generally speaking, minimum period and length （Tmin, Lmin） of atmospheric waves, which may be simulated by the model, are determined by the time step and grid length （△t, △X）, such as Tmin=4△t, Lmin= 4△X. Serious error occurring in calculating the shorter wave （T〈4△t） is inevitable as shown in the above case. Tmin, will match with Lmin when △t=△X/C0, where CO is the wave speed. If △t〉〉△X/C0, only waves with L〉4△t · Co can be accurately simu

关 键 词：半拉格朗日半隐式格式 非线性源汇项 时步 

分 类 号：P435[天文地球—大气科学及气象学]