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1.
Three-Step Difference Scheme for Solving Nonlinear Time-Evolution Partial Differential Equations 
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下载免费PDF全文 In this paper, a special three-step difference scheme is applied to the solution of nonlinear time-evolution equations, whose coefficients are determined according to accuracy constraints, necessary conditions of square conservation, and historical observation information under the linear supposition. As in the linear case, the schemes also have obvious superiority in overall performance in the nonlinear case compared with traditional finite difference schemes, e.g., the leapfrog（LF） scheme and the complete square conservation difference（CSCD） scheme that do not use historical observations in determining their coefficients, and the retrospective time integration（RTI） scheme that does not consider compatibility and square conservation. Ideal numerical experiments using the one-dimensional nonlinear advection equation with an exact solution show that this three-step scheme minimizes its root mean square error（RMSE） during the first 2500 integration steps when no shock waves occur in the exact solution, while the RTI scheme outperforms the LF scheme and CSCD scheme only in the first 1000 steps and then becomes the worst in terms of RMSE up to the 2500th step. It is concluded that reasonable consideration of accuracy, square conservation, and historical observations is also critical for good performance of a finite difference scheme for solving nonlinear equations. 相似文献
2.
在数值预报和数值模拟中,描述空间微分项的最主要的方法是有限差分法,但使用差分方法会引入截断误差.伍荣生1979年指出,通过在原物理场的基础上构造一个新的物理场,替代原物理场进行差分计算,可以达到减小误差的目的.该文是伍荣生1979年工作的继续,目的在于解释伍荣生1979年所构造的差分格式并得到更为一般化的差分格式.文中给出新的差分格式结合了经典有限差分方法的快速计算和谱方法的高精度的优点.如果在一个给定的网格上对气象要素场进行离散傅里叶级数展开,则基函数(正弦或余弦)的频谱是事免已知的.作者将伍荣生1979年构造物理场的方法视为对物理场的一次平滑,探讨了获取二次平滑场、多次平滑的一般化方法.获取平滑场的基奉原理是使得在固定频谱上的差分逼近程度达到最优.通过对频谱上的累计误差的下降速度分析表明,平滑次数的上限为3次.数值分析的结果表明,二次平滑的最大误差是未作任何平滑的最大误差的0.04倍,在使用相同计算代价的情况下,二次平滑的最大误差是经典的差分格式的0.3倍.平流试验的结果也表明,新的差分格式即一次平滑、二次平滑方案的结果远远优于经典的差分格式.新的差分格式意义在于,在不加密网格的情况下提供了一条提高数值计算精度的途径. 相似文献
3.
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
4.
本文提出一种基于百分位映射,使用实时和历史资料联合订正模式定量降水短时订正预报技术,并与仅使用历史资料或实时资料的订正效果进行对比。结果表明:三种方案均能有效订正模式原始降水预报偏差,提高0~12 h降水预报准确率。对于晴雨预报,采用联合订正方案,预报效果最优。在0~7 h预报时效内,仅采用实时资料的订正方案准确率明显优于仅采用历史资料的订正方案,在8~12 h预报时效内,后者准确率稍高。所有预报时效内,仅采用实时资料的订正方案降水预报范围较仅采用历史资料的方案略偏大。对于较强降水预报,采用联合订正方案准确率为三种方案最优,仅采用实时资料的方案预报准确率虽优于仅采用历史资料的方案,但预报范围及量级较实况明显偏大。 相似文献
5.
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6.
This paper introduces a new consistent dissipation operator. It is based on the explicit square conservation scheme and the theory of consistent dissipation. The operator makes full use of the advantages of the Leap-frog scheme, i.e., its second order time precision and its explicit solution manner. Meanwhile, it overcomes the fatal disad-vantage, the absolute instability in computations, of the scheme. When it is applied to the explicit square conservation scheme, the time precision of the scheme reaches to third order. Especially, the computational stability of this scheme is as good as the third order explicit Runge-Kutta scheme. The CPU time required in computations by the scheme is less than that required by the explicit square conservation scheme with the consistent dissipation operator constructed from the Runge-Kutta method. Therefore, the new operator is an economical one. The application of the operator to the improvement of the dynamical model of the L2IAP AGCM shows its time-saving property and its good effects 相似文献
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8.
In this paper,a kind of explicit difference scheme to solve nonlinear evolution equations,perfectly keeping the square conservation by adjusting the time step interval,is constructed,from the comprehensive maintenance of the advantages of the implicit complete square conservative scheme and the explicit instantaneous square conservative scheme.The new schemes are based on the thought of adding a small dissipation,but it is different from the small dissipation method.The dissipative term used in the new schemes is not a simple artificial dissipative term,but a so-called(time) harmonious dissipative term that can compensate for the truncation errors from the dissociation of the time differential term.Therefore,the new schemes may have a high time precision and may acquire a satisfactory effect in numerical tests. 相似文献
9.
一个压力坐标下的海洋环流模式 总被引：5，自引：0，他引：5
A new oceanic general circulation model in pressure coordinates is formulated. Since the bottom pressure changes with time, the vertical coordinate is actually a pressure-σ coordinate. The numerical solution of the model is based on an energy-conservation scheme of finite difference. The most important new feature of the model is that it is a truly compressible ocean model and it is free of the Boussinesq approxima tions. Thus, the new model is quite different from many existing models in the following ways: 1) the exact form of mass conservation, 2) the in-situ instantaneous pressure and the UNESCO equation of state to calculate density, 3) the in-situ density in the momentum equations, 4) finite difference schemes that conserve the total energy. Initial tests showed that the model code runs smoothly, and it is quite stable. The quasi-steady circulation patterns generated by the new model compare well with existing models, but the time evolution of the new model seems different from some existing models. Thus, the non-Boussinesq models may provide more accurate information for climate study and satellite observations. 相似文献
10.
变步长显式完全平方守恒差分格式 总被引：8，自引：0，他引：8
综合隐式完全平方守恒差分格式和显式瞬时平方守恒差分格式的优点，针对一类非线性发展方程构造了一种通过自动调节时间步长来保持平方守恒性的显式差分格式。它基于加小耗散的思想，但又与小耗散法有所不同。本文取的耗散项不是一般的人工耗散，而是取能够弥补由于时间离散所产生的截断误差的所谓（时间）协调耗散。因此，该格式具有较高的时间精度。在数值试验中，该类格式可取得满意的效果。 相似文献
11.
The calculation scheme of the smoothed-level and hybrid (SLEVE-hybrid for short) coordinates in numerical forecasting model is not limited to one. It is divided into the semi-analytical scheme and the finite differential scheme in
terms of the various differential methods of the coordinate deformation variables. Comparing the dynamic equation and the long-time batch simulation results of the two schemes, the present study draws the following conclusions. The first-
order finite difference accuracy of the coordinate deformation variables in the finite differential scheme is theoretically lower than that in the semi-analytical scheme. The larger the vertical gradient of the layer thickness is, the larger the
relative errors of the finite differential scheme are. The long-time batch simulation test in the GRAPES model dynamic core demonstrates that the bias of the temperature and the geopotential height in the semi-analytical scheme is smaller
under the default layering, while the simulation difference of the two schemes is greatly reduced when the layering is more uniform. 相似文献
12.
《热带气象学报(英文版)》2021,(2)
The calculation scheme of the smoothed-level and hybrid(SLEVE-hybrid for short) coordinates in numerical forecasting model is not limited in number. It is divided into the semi-analytical scheme and the finite differential scheme in terms of the various differential methods of the coordinate deformation variables. Having compared the dynamic equation and the long-time batch simulation results of the two schemes, the present study draws the following conclusions. The first-order finite difference accuracy of the coordinate deformation variables in the finite differential scheme is theoretically lower than that in the semi-analytical scheme. The larger the vertical gradient of the layer thickness is, the larger the relative errors of the finite differential scheme are. The long-time batch simulation test in the GRAPES model dynamic core demonstrates that the bias of the temperature and the geopotential height in the semianalytical scheme is smaller under the default layering, while the simulation difference of the two schemes is greatly reduced when the layering is more uniform. 相似文献
13.
将任一中尺度区域的平均瞬间径流率考虑为区域平均降水量和地表土壤层水分渗透垦的余项.根据降水量在地理空间上分布的实测资料拟合其空间概率密度函数(PDF),并结合土壤入渗物理过程的数学描述及其经验公式,精确估计出地表土壤渗透率及其空间分布,由此建立区域地表径流率的统计-动力学估计方案.换言之,区域内地表产流率可视为区域平均降水量与区域平均的土壤下渗量之差值,而区域内土壤的平均下渗量又町分为非饱和区和饱和区两部分的下渗量来分别计算.就陆面水分循环的物理过程而言,地表入渗现象是在一定的下垫面特性基础上,由一定的水分供应源而形成的.根据大气降水向地表层输送水分的物理过程,在满足植被表层覆盖需水(截流水)和地表层土壤人渗水基础上,多余的降水量才会形成地表径流.凶此,推求地表产流率的主要关键在于地表土壤层需水量.为此奉文根据土壤水分通量方程推导出水分入渗公式.又从描述土壤水分和降水的空间PDF出发,推导出非均匀土壤含水量及降水气候强迫所形成的次网格尺度区域平均径流率计算公式.利用长江三角洲地区1996年降水量和土壤特性等实测资料建立区域平均地表径流率的估计公式,并对其影响凶素进行敏感性试验.结果表明,该方法与用Mosaic方法计算的区域径流率(或产流率)结果十分接近.由此可见,该文提出的降水气候强迫下非均匀地表区域平均径流的这种统计-动力参数化方案,具有相当的可靠性与可行性. 相似文献
14.
基于Prata晴空大气下行长波辐射参数化方案,针对其在高原地区及可降水量较小地区理论精度较差的缺点,考虑不同高度的大气柱发射的长波辐射量不同,提出了三种考虑气压的大气下行长波辐射参数化方案,通过全球ERA-5再分析数据进行最小二乘拟合确定经验常数并在全球不同区域对其适用性进行了分析.模拟结果表明,考虑气压的参数化方案有... 相似文献
15.
两步保形平流方案在高分辨率球面经纬网格下的跳点差分试验 总被引：1，自引：0，他引：1
尝试用一个基于有限差分的两步保形平流方案（TSPAS）替代美国国家大气研究中心第5版公用大气模式（NCAR-CAM5）欧拉-谱动力框架中的半拉格朗日传输（SLT）平流方案,并针对不同分辨率版本,计算水汽等物质的传输过程。通过设计保证守恒性的跳点差分法,解决了基于经纬网格的模式在高分辨率下由于极区纬向格距过小而造成的差分方案积分时间步长过短的问题,使得TSPAS在高分辨率下仍然可以使用较大的时间步长。理想试验表明：（1）跳点TSPAS在守恒性、数值精度（量级上）、保形性等方面均较好地保持了原TSPAS的特点,而积分步长可增大到与CAM5-SLT相同,比原TSPAS提高超过一个数量级;（2）较半拉格朗日传输方案,尽管TSPAS的耗散更大,但是在相同时间步长下更省时,且改进了半拉格朗日传输求解平流方程造成的不守恒问题。CAM5的比较试验表明：（1）采用跳点TSPAS的模式结果与非跳点计算结果相当,在高纬度跳点区域也并未出现模拟异常;（2）在高分辨率下,采用跳点TSPAS方案的CAM5模拟结果与原模式结果相近,并初步显示对东亚青藏高原南侧的虚假降水有所抑制。该工作确保了基于欧拉通量差分型的TSPAS在高分辨率模式下的大时间步长稳定积分,为解决有限差分方法在高分辨率模式发展中的相关计算问题提供了启示,为后续针对东亚地区的模式性能改进奠定了基础。 相似文献
16.
传统的高阶精度有限差分格式通常是在均匀网格的基础上推导得到的,在非均匀网格的情况下它会出现精度退化的问题。基于泰勒展开方法构造了一种适用于非均匀网格的2阶、4阶和6阶精度中央有限差分方案,利用Burgers方程和一维平流方程对新方案的性能进行测试,着重分析新方案对其误差大小及分布形态的改进效果。数值模拟结果表明:在非均匀网格下,提高差分方案的精度可明显减小数值解误差(降低了70%~88%),特别是当差分精度从2阶提高到4阶的时候。同时,高阶精度方案在梯度变化较大或者网格距较粗区域的模拟结果更有优势,4阶和6阶精度方案在以上区域的误差远小于2阶精度方案。方案可用于提高数值天气预报模式中非均匀分层模式的垂直差分计算精度。 相似文献
17.
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
18.
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
19.
Construction of high-order difference schemes based on Taylor series expansion has long been a hot topic in computational mathematics, while its application in comprehensive weather models is still very rare. Here, the properties of high-order finite difference schemes are studied based on idealized numerical testing, for the purpose of their application in the Global/Regional Assimilation and Prediction System(GRAPES) model. It is found that the pros and cons due to grid staggering choices diminish with higher-order schemes based on linearized analysis of the one-dimensional gravity wave equation. The improvement of higher-order difference schemes is still obvious for the mesh with smooth varied grid distance. The results of discontinuous square wave testing also exhibits the superiority of high-order schemes. For a model grid with severe non-uniformity and non-orthogonality, the advantage of high-order difference schemes is inapparent, as shown by the results of two-dimensional idealized advection tests under a terrain-following coordinate. In addition, the increase in computational expense caused by high-order schemes can be avoided by the precondition technique used in the GRAPES model. In general, a high-order finite difference scheme is a preferable choice for the tropical regional GRAPES model with a quasi-uniform and quasi-orthogonal grid mesh. 相似文献
20.
文中指出了分解算法中的两个问题:(1)为了使算法获得最佳效果,除按快、慢过程分解方程外,进一步的分解应按什么原则?(2)时间离散是否可以任意,如果不然,应采取什么形式?针对这两个问题得到的研究结果是:和一般设计简化模式一样,分解后的方程应保持原方程的重要物理性质,特别是其整体性质(如能量守恒和质量守恒等),而且,其分解后方程的解还应和原方程的解一致,至少对其中重要的解应一致.至于时间离散,在差分的情况则应采用二时间层格式;如采用三时间层格式,则会导致差分方程(或差分微分方程)和偏微分方程的不相容. 相似文献