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基于计算准稳定的概念来分析强迫耗散非线性方程显式差分格式的计算稳定性，给出强迫耗散非线性大气方程组显示差分格式计算准稳定的判据，为设计强迫耗散非线性大气方程组计算稳定的显式差分格式提供了新的思路和理论依据。 相似文献
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线性与非线性发展方程计算稳定性的比较分析 总被引：21，自引：0，他引：21
针对性与非线性发展方程的几种差分格式，以一维线性和非线性平流方程为例，对线性与非线笥发展方程差分格式的计算稳定性进行了比较分析，揭示了差分格式结构和初值形式与计算稳定性的关系。理论分析和数值试验证明，线性与非线性发展方程差分格式的计算稳定性在本质上是完全不同的。 相似文献
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强迫耗散非线性发展方程准完全平方守恒格式的构造 总被引：5，自引：0，他引：5
从描述大气和海洋运动的强迫耗散非线性发展方程出发，对强迫耗散非线性大气和海洋方程组显式差分格式的计算稳定性进行了分析，构造了一类强迫耗散性发展方程的显式准完全平方守恒差分格式，理论分析和数值试验证明，这类显式准完全平方守恒差分格式是计算稳定的．值得推广应用。 相似文献
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本文用差分模拟绝对涡度守恒定律,构成正压涡度方程的两类差分格式:积分守恒型格式和相当于准拉格朗日型格式。前一类型格式的显式部分是条件稳定的,隐式部分是无条件稳定的。后者至为无条件稳定的显式格式,可以依据实际需要和可能,来放大无条件稳定格式的时间步长。 本文还根据格式的计算要求,讨论了“风”场的计算和平滑问题,以及差分方程的边、初条件(计算边、初条件)的给法。并通过理想场计算和实例预报,检验了几种显式格式的计算效果。 相似文献
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天气数值预报工作中所用的初始方程显式差分格式,时间步长取得很短,实际应用很不方便。比如,空间步长取300公里,时间步长只能用10分钟。本文提出一种新型显式差分格式,其计算稳定性不受时间步长(τ)和空间步长(d)大小的限制,由|λ_e|τ/d(e=1,2,3)的整数部分m_e=[|λ_e|τ/d],控制执行“浮动”计算,保持计算稳定。这种差分格式曾用104电子计算机作检验计算,空间步长用25公里,时间步长取20分钟,计算过程稳定,结果精度较高,可与文献[1]中的结果相比较。这表明,初始方程的差分计算,适当延长时间步长是有可能的。 相似文献
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再论发展方程差分格式的构造和应用 总被引：40，自引：8，他引：32
【摘 要】本文把一大类大气、海洋方程归结为一种发展方程,具体构造了若干定时间步长的显式完全平方守恒差分格式。并证明在一定条件下,这类格式也具有能量守恒、“广义能量”守恒和“平均尺度”守恒的特性,它表明这类格式具有较好的计算稳定性和省时性。文中还探讨了显式平方守恒格式与隐式平方守恒格式之间的密切联系。最后给出了令人满意的用四波的R-H波作数值检验的结果。 相似文献
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模式低空急流结构与水汽输送精度的数值试验 总被引：1，自引：0，他引：1
本文所使用的中尺度模式ＭＭ４改进了水汽平流的计算精度，引入了Ｐｒａｔｈｅｒ和Ｂｏｔｔ两种高精度正定闰流差分格式。首先探讨了仅考虑模式平流过程的情况下不同平流差分格式的误差特征对模式结果的可能影响。结果显示：ＭＭ４中原有的水汽平流差分格式在水汽梯度较大处产生水汽负值，而引入搞精度格式能正确模拟水汽为分布的特征，对不同精度的水汽平流分格式作了数值试验，不同格式下模式的低突急流结构有较明显差别，水汽输送 相似文献
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进一步讨论了有关非线性不稳定的一些问题,其主要内容有： １．考察了有代表性的三类发展方程,指出其对应的差分格式是否出现非线性计算不稳定,与原微分方程解的性质密切相关。 ２．进一步讨论了带周期边条件的守恒型差分格式的非线性计算稳定性问题,总结了克服非线性不稳定的有效措施。 ３．以非线性平流方程为例,着重分析了带非周期边条件的非守恒差分格式的非线性计算稳定性问题,给出了判别其计算稳定性的“综合分析判别法”。 相似文献
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Y. Wang 《Meteorology and Atmospheric Physics》1996,61(1-2):27-38
Summary The classical forward-in-time upstream advection scheme for uniform flow field has been extended to include non-uniform and time-dependent advective flow. This generalised scheme is described in one dimension for an advective flow which varies both in time and in space. The classical upstream advection scheme is only first-order accurate both in time and in space if the advective flow is not uniform. Higherorder accuracy in both time and space, however, can be easily obtained in the generalised scheme.This generalised scheme with third-order accuracy is applied to the one-dimensional inviscid Burgers equation (socalled self-advection problem), two-dimensional steady flow, and to a time-split shallow water equation model. The results are compared with those obtained from the Takacs' (1985) scheme and from a standard third-order semi-Lagrangian scheme, and also with those obtained from the fourth-order Lax-Wendroff scheme of Crowley (1968) in the time-split shallow water equation model. It is shown that the generalised scheme performs as well as, but is more efficient than, the standard semi-Lagrangian scheme with same order. It is much more accurate than the Takacs' scheme which has large dissipation errors, especially for the flow with strong deformation. In contrast, the generalised scheme has very weak dissipation and has much better dispersion and shapeconserving properties. Although the fourth-order Lax-Wendroff scheme has higher accuracy and can give more accurate numerical solutions for uniform advective flow or solid rotational flow (Crowley, 1968), it is inferior to the generalised third-order scheme for non-uniform flow with strong deformation or large spatial gradients. This generalised scheme, therefore, has considerable application potential in different numerical models, especially for the models using time-split algorithms.With 8 Figures 相似文献
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Liu Ruizhi 《大气科学进展》1985,2(2):178-188
In this paper, a numerical test is carried out by using a six-level implicit primitive equation model de-fined in a π coordinate. The model equations are solved with nonlinear iterated method, yielding fairly good results.However, it is time-consuming to solve the model with iterated method. Thus, this model is restored to the advective scheme and solved by means of a split method. Several actual examples are forecasted, which have yielded good results. 相似文献
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SPLIT SEMI-IMPLICIT INTEGRATION OF TROPICAL LIMITED AREA MULTI-LEVEL PRIMITIVE EQUATION MODEL 
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下载免费PDF全文 A tropical limited area multi-level primitive equation model,in which the time integral is performed with a split semi-implicit scheme,is presented.The operating time is shortened to one-third of the time the explicit scheme needs.The results of operational experiments show that the model is stable in computation and capable of producing satisfactory forecast for tropical systems.Besides synoptic reports,data derived from other sources are used so as to improve the forecast,especially over tropical oceans where conventional data are scarce. 相似文献
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众所周知,积云尺度和大尺度运动的水平和时间尺度相差甚远,因此,在较大尺度的网格点上应借助于参数化方法来描述积云尺度的运动。比如,假定对流凝结加热与潮湿空气的辐合量有关(郭晓岚1965,1974),或者假定与涡度或垂直速度成正比(李崇银1984),并且依赖确定的加热参数的垂直分布廓线。我们用李崇银(1984)的参数化方案对台风发展的数值模拟表明,加热强度参数和垂直分布廓线对模拟结果非常敏感。因此,有必要寻求其他途径或参数化方法。 相似文献
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In this paper,we have suggested several interpolating formulae which are convinient for vector computers to perform vector calculation.Analysis shows that for a simple advective problem,the semi-Lagrangian schemes constructed with these formulae are linearly unconditionally stable.Moreover,we have discussed the nonlinear computational chaos in the semi-Lagrangian schemes.It is found that for a simple nonlinear advective problem,we can introduce physically unreal and direct interaction of three or more waves.Numerical tests indicate that this phenomenon has certain influence on the simulated results of two-dimensional Benard convection. 相似文献
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针对一类大气、海洋问题，从算子方程出发，在显式完全平方守恒差分格式的基础上提出两种变时间步长的差分算法，使数值计算更加有效。在人工调节时间步长法中，通过人为控制方程中算子能量变化的办法调整时间步长；在自动调节时间步长法中，通过数值试验自动比较出所构造差分格式稳定性的好坏，将它与泰勒展开法及分解算法进行混合应用，验明了自动调节时间步长法具有综合判断差分格式好坏的功能，并得出一些有意义的结论。 相似文献
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An experimental micrometeorological set-up was established at the CARBOEURO-FLUX site in Tharandt, Germany, to measure all relevant variables for the calculation of the vertical and horizontal advective fluxes of carbon dioxide. The set-up includes two auxiliary towers to measure horizontal and vertical CO2 and H2O gradients through the canopy, and to make ultrasonic wind measurements in the trunk space. In combination with the long-term flux tower an approximately even-sided prism with a typical side-length of 50 m was established. It is shown that under stable (nighttime) conditions the mean advective fluxes have magnitudes on the same order as the daily eddy covariance (EC) flux, which implies that they play a significant, but not yet fully understood, role in the carbon budget equation. The two advective fluxes are opposite and seem to cancel each other at night (at least for these measurements). During the day, vertical advection tends to zero, while horizontal advection is still present implying a flow of CO2 out of the control volume. From our measurements, a mean daily gain of 2.2 gC m–2 d–1 for the horizontal advection and a mean daily loss of 2.5 gC m–2d–1 for the vertical advection is calculated for a period of 20 days. However the large scatter of the advective fluxes has to be further investigated. It is not clear yet whether the large variability is natural or due to measurement errors and conceptual deficiencies of the experiment. Similar results are found in the few comparable studies. 相似文献