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An Improved Splitting Method 总被引：3，自引：0，他引：3
In this paper, an improved splitting method, based on the completely square-conservative explicit difference schemes, is established. Not only can the time-direction precision of this method be higher than that of the traditional splitting methods but also can the physical feature of mutual dependence of the fast and the slow stages that are calculated separately and splittingly be kept as well. Moreover, the method owns an universality, it can be generalized to other square-conservative difference schemes, such as the implicit and complete ones and the explicit and instantaneous ones. Good time benefits can be acquired when it is applied in the numerical simulations of the monthly mean currents of the South China Sea. 相似文献
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In order to meet the needs of work in numerical weather forecast and in numerical simulations for climate change and ocean current, a kind of difference scheme in high precision in the time direction developed from the completely square-conservative difference scheme in explicit way is built by means of the Taylor expansion. A numerical test with 4-wave Rossby-Haurwitz waves on them and an application of them on the monthly mean current the of South China Sea are carried out, from which, it is found that not only do the new schemes have high harmony and approximate precision but also can the time step of the schemes be lengthened and can much computational time be saved. Therefore, they are worth generalizing and applying. 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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采用新的均匀三点中心约束多矩有限体积方法（3-point Multi-moment Constrained finite-Volume scheme for Uniform Points with Center Constraints, MCV3_UPCC）,发展了一个三阶正定守恒的平流模式。三点多矩有限体积方法在单网格内定义等距的3个自由度,采用多矩约束条件并通过控制方程获得时间演变方程。新的三点中心约束多矩方法能在单网格内采用等距的3个点值及中心一阶、二阶导数作为约束条件进行空间4次多项式数值重构,获得3个自由度的时间演变方程;所构建的新数值方案具有三阶精度,边界通量连续性保证了其数值严格守恒。为了抑制该方法的非物理数值振荡,引入了边界保型限制器技术,它能够把数值解控制在既定物理场最小值（最小值为0时则保持数值正定）与最大值之间。数值试验表明新发展的三阶平流模式具有良好的计算精度,能够严格保持数值解的正定性和守恒性,同其他高精度平流模式相当,在实际大气模式水汽等平流输送应用中具备良好的发展潜力。 相似文献
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Pengfei WANG 《大气科学进展》2017,34(12):1461-1471
Based on the Taylor series method and Li's spatial differential method, a high-order hybrid Taylor–Li scheme is proposed.The results of a linear advection equation indicate that, using the initial values of the square-wave type, a result with thirdorder accuracy occurs. However, using initial values associated with the Gaussian function type, a result with very high precision appears. The study demonstrates that, when the order of the time integral is more than three, the corresponding optimal spatial difference order could be higher than six. The results indicate that the reason for why there is no improvement related to an order of spatial difference above six is the use of a time integral scheme that is not high enough. The author also proposes a recursive differential method to improve the Taylor–Li scheme's computation speed. A more rapid and highprecision program than direct computation of the high-order space differential item is employed, and the computation speed is dramatically boosted. Based on a multiple-precision library, the ultrahigh-order Taylor–Li scheme can be used to solve the advection equation and Burgers' equation. 相似文献
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简要介绍中国科学院大气物理研究所七十多年来在理论与计算地球流体力学方面的若干研究及其新的进展.在理论地球流体力学方面,介绍了长波动力学及线性稳定性问题、弱非线性理论及行星波动力学以及用Arnold方法(能量-Casimir方法)研究大气和海洋中各种流体运动的非线性稳定性问题的成果.此外,对扰动演变、扰动和基流相互作用及热带大气动力学中的第二类不稳定条件(CISK)也作了简要的介绍.在计算地球流体力学方面,主要内容包括:用物理观点和数学分析相结合的方法阐述了造成计算紊乱和计算不稳定的机理,论证计算稳定性、算 相似文献
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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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利用高阶Li空间微分方案(Li, 2005),实现了时间积分为3～6阶Runge-Kutta-Li(RKL)格式的求解算法。二维线性平流方程的试验结果表明:在计算稳定的条件下,各阶算法的计算误差随时间的推移基本上是线性增加的。非转动背景场的平流算例中（高斯型的初值）,高阶RKL算法可以取得较好的计算效果。与3、4、5、6阶RK算法配合的Li空间差分方案有效阶数可以达到5、7、9、10阶。RK 算法的阶数为5（6）阶时,总误差控制在10-7（10-8）以内。随RK阶数增加Li微分的有效阶数有增加趋势,且总误差逐渐减小。定常转速的背景场算例中（偏心的高斯型初值）,当RK阶数为3时,最优空间差分阶数为10;相应的阶数为4、5、6时对应的空间最优阶为16,22,22,总计算误差可以控制在10-15～10-16。随着精度的提高,误差的绝对值减小很迅速,说明算法是非常有效的。对于圆锥型初值（定常转速的背景场）,4、5、6阶RK算法和3阶算法的效果差不多。高阶算法对此类具有导数不连续点的算例,效果不如高斯初始场好,结果不能保持正定,有些地方误差出现下冲和上翘。随着空间差分精度的提高,非正定的解数量和数值减小,误差的绝对值减小,说明了算法在一定程度上是有效的,但并不适合追求极高的算法阶数。这与谱方法中的导数不连续问题有些相似,误差的产生主要源于导数的不连续性,差分类方法仅能获得与导数连续性阶数相当的算法精度。各种算例中,采用恰当的边界条件是必要的,例如旋转背景场算例,比较适合使用无穷远边界条件,否则会出现计算不稳定或无法将计算误差控制到较小的范围内。 相似文献
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大气粒子散射相函数的参数化是大气辐射传输参数化的重要组成部分。文中全面比较了大气粒子的HenyeyGreenstein(HG)方案和双Henyey-Greenstein(DHG)方案,并在四流球谐函数展开累加法中,应用这两种相函数参数化方案计算气溶胶、云、霾粒子的反射率、透射率或吸收率。该研究结果表明:HG方案无法表现相函数的后向峰值,因而其计算的大气粒子反射率和透射率精度较差;DHG方案能较好地表征相函数的整体特征,但是该方案计算的相函数易出现后向异常峰值或为负值,并导致计算得到的气溶胶、云、霾粒子的反射率和透射率精度甚至会低于HG方案。对DHG方案进行进一步研究,提出了改进的DHG方案(MDHG)。MDHG方案计算结果稳定,并能很好表征相函数的前向和后向峰值的特征,其计算的大气粒子的反射率和透射率精度也较高。因此,MDHG方案是一种理想的相函数参数化方案。 相似文献
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Designed for grid point systems, the traditional semi-Lagrangian semi-implicit scheme is not mass-conserving and can lead to significant solution errors. In the present study, a finite-volume semi-Lagrangian semi-implicit scheme (hereafter “FVSLSI”) is designed for the Yin-Yang mesh and tested in a barotropic shallow water model in the spherical coordinate system. Three test cases, i.e. the advection of a solid body, a steady state nonlinear zonal geostrophic flow and the deformation flow, are simulated to compare the performance of the FVSLSI with that of the traditional semi-Lagrangian scheme (hereafter “SL”) from perspectives of shape preservation, mass conservation, normalized bias, and convergence rate. Results indicate that the FVSLSI performs better than the SL in mass conservation and shape preservation. The bias by the FVSLSI is smaller than that by the SL, while the rate of convergence by the FVSLSI is larger than that by the SL. The FVSLSI also allows large time step. Therefore, the FVSLSI is suggested to be distributed to communities that are developing atmospheric/oceanic models. 相似文献
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Generalized Square Conservative Multistep Finite Difference Scheme Incorporating Historical Observations 
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下载免费PDF全文 In this paper,a multistep finite difference scheme has been proposed,whose coefficients are determined taking into consideration compatibility and generalized quadratic conservation,as well as incorporating historical observation data.The schemes have three advantages:high-order accuracy in time,generalized square conservation,and smart use of historical observations.Numerical tests based on the one-dimensional linear advection equations suggest that reasonable consideration of accuracy,square conservation,and inclusion of historical observations is critical for good performance of a finite difference scheme. 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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高精度迎风偏斜格式的比较与分析 总被引：1，自引：0，他引：1
利用一种具有任意阶精度的一般显式有限差分公式构造出高精度迎风偏斜格式，并利用 Fourier分析法评估了这些迎风偏斜格式的耗散误差与频散误差。结果表明，偶阶精度格式的数值相速度快于实际相速度，而奇阶精度格式的数值相速度慢于实际相速度。并且，偶阶精度格式的耗散误差与频散误差低于相邻的奇阶精度格式。为了检验这些格式的计算性能，在一维问题上进行了应用。首先，考虑恒定风场条件下的一维平流试验。主要选择两种不同的初始条件来评价数值格式的精度，这两种试验问题分别是高斯函数、方波函数。试验结果表明，随着数值格式精度的提高，数值格式的误差逐渐减小。而对于高于六阶精度的格式来说，改进的程度并不是很大。其次，应用各阶格式到具有两种不同初始条件的无粘Burgers方程。数值结果表明，随着数值格式阶数的增加，数值结果也得到了明显改进。而对于高于六阶精度的格式来说，进一步的变化并不明显。总之，在兼顾效率与精度条件下六阶迎风偏斜格式是最好的。 相似文献
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The earth system model of intermediate complexity CLIMBER-3α. Part I: description and performance for present-day conditions 总被引：1，自引：0，他引：1
Marisa Montoya Alexa Griesel Anders Levermann Juliette Mignot Matthias Hofmann Andrey Ganopolski Stefan Rahmstorf 《Climate Dynamics》2005,25(2-3):237-263
We herein present the CLIMBER-3α Earth System Model of Intermediate Complexity (EMIC), which has evolved from the CLIMBER-2 EMIC. The main difference with respect to CLIMBER-2 is its oceanic component, which has been replaced by a state-of-the-art ocean model, which includes an ocean general circulation model (GCM), a biogeochemistry module, and a state-of-the-art sea-ice model. Thus, CLIMBER-3α includes modules describing the atmosphere, land-surface scheme, terrestrial vegetation, ocean, sea ice, and ocean biogeochemistry. Owing to its relatively simple atmospheric component, it is approximately two orders of magnitude faster than coupled GCMs, allowing the performance of a much larger number of integrations and sensitivity studies as well as longer ones. At the same time its oceanic component confers on it a larger degree of realism compared to those EMICs which include simpler oceanic components. The coupling does not include heat or freshwater flux corrections. The comparison against the climatologies shows that CLIMBER-3α satisfactorily describes the large-scale characteristics of the atmosphere, ocean and sea ice on seasonal timescales. As a result of the tracer advection scheme employed, the ocean component satisfactorily simulates the large-scale oceanic circulation with very little numerical and explicit vertical diffusion. The model is thus suited for the study of the large-scale climate and large-scale ocean dynamics. We herein describe its performance for present-day boundary conditions. In a companion paper (Part II), the sensitivity of the model to variations in the external forcing, as well as the role of certain model parameterisations and internal parameters, will be analysed. 相似文献
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Argo大洋观测资料的同化及其在短期气候预测和海洋分析中的应用 总被引：3，自引：0，他引：3
国际Argo(Array for Real-time Geostrophic Oceanography)计划的实施,提供了前所未有的全球深海大洋0～2000 m水深范围内的海水温度和盐度观测资料,在大气和海洋科研业务中应用这一全新的资料,是深入认识大气和海洋变异、提高我国气候预测、海洋监测分析和预报能力的一个关键所在.通过开发非线性温—盐协调同化方案和利用同化高度计资料来调整模式的温度和盐度场,建立了可同化包括Argo等多种海洋观测资料的全球海洋资料变分同化系统,提高了对全球海洋的监测分析能力.实现了海洋资料同化系统与全球海气耦合模式的耦合,显著提高了短期气候预测水平.利用Argo资料改进了海洋动力模式中的物理过程参数化方案,有效提高了海洋模式对真实大洋的模拟能力和对厄尔尼诺/拉尼娜的预测能力.开发了利用Argo浮标漂流轨迹推算全球海洋表层和中层流的方法,提高了推算的全球表层流、中层流资料质量,有效弥补了洋流观测的匮乏. 相似文献
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利用有限区域非静力MM5模式, 分析了显式降水方案对于2003年7月4—5日南京暴雨数值模拟的不确定性影响。采用混合方案模拟此次暴雨时, 这种不确定性决定于显式和隐式方案的相互协调性及敏感性; 隐式方案基本决定了雨带的整体的空间分布, 而显式方案对于降水型及降水量起到一定的调节作用, 调节的程度与选择的参数化方案有关; 采用隐式方案Grell和KF2模拟此次暴雨时, 应考虑不同的显式方案对于降水模拟的不确定性的影响。 相似文献