共查询到18条相似文献，搜索用时 187 毫秒
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为提高数值求解大气方程的速度, 研究了预处理JFNK（Jacobian-Free Newton-Krylov）方法及其在大气方程中的应用。这是一种非线性外循环Newton迭代与线性内循环Krylobv迭代相结合的快速算法,其优点是进行外循环Newton迭代时不要求Jacobian矩阵的形成和存储;它的有效性取决于内循环中线性系统的预处理。首先介绍了JFNK算法,然后以浅水波方程为例,描述了非线性残值的形成、预处理矩阵的构造及其在JFNK算法中的应用。试验结果表明：对内循环线性系统进行适当的预处理,能大幅度提高JFNK算法的运算速度。因而,JFNK是一种值得在大气方程中推广应用的方法。 相似文献
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数值预报模式动力框架发展的若干问题综述 总被引：14，自引：3，他引：11
作者就大气数值模式动力框架发展的几个问题做了回顾和展望.关于模式地形的处理,讨论了"地形追随"(terrain-following)坐标和"台阶地形"(step-mountain)η坐标的优点、问题和对策.关于物理量守恒格式的构造,回顾了从"瞬时"守恒到隐式、显示和半隐式完全(包括时间离散)守恒格式的发展和近况,介绍了加速非线性全隐式问题迭代收敛的途径.还讨论了半拉格朗日守恒格式的构造问题.最后,对目前广泛使用的全球谱模式,讨论了其长处、局限和发展前景,并简单介绍了谱元方法. 相似文献
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在原始方程模式的显式积分中,为使高频重力波保持计算稳定性,时间步长必须取得很小以满足CFL稳定性判据。半隐式积分方案较之显式积分可以使用较大的时间步长,因而提高了计算效率。但是,与半隐式方案相伴随的是要解一Helmholtz方程,这个方程的求解在积分过程中占有相当比重,这一点在差分模式中尤其明显。因此,消除Helmholtz方程是进一步提高时间积分效率的一个重要方面。 相似文献
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采用隐式立方样条计算平流过程的数值模式及理想实验 总被引：1，自引：0，他引：1
本文介绍了一种用隐式立方样条求解平流方程的数值方法,并从理论上对其无条件稳定性进行了证明,在此基础上建立了一个在地形坐标系下的两维原始方程模式,模式在行星边界层参数化中引入了湍流动能方程,在模式顶部引入了吸收层.数值实验表明:模式有较好的计算稳定性,对较高的模式水平分辨率和复杂地形均有较强的适应能力;对复杂地形和下垫面非均匀热源条件下中尺度系统的模拟能获得合理的结果,并具有较高的精确度. 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
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针对多变量方程误差滑动平均系统,利用最小二乘原理和迭代搜索原理,给出了增广随机梯度辨识方法、递推增广最小二乘辨识方法、梯度迭代辨识方法和最小二乘迭代辨识方法.针对多变量方程误差滑动平均系统和多变量方程误差自回归滑动平均系统,将多变量系统分解为一些子系统,利用耦合辨识概念,讨论了梯度迭代辨识方法、部分耦合（子系统）梯度迭代辨识方法、子系统最小二乘迭代方法和部分耦合子系统最小二乘迭代辨识方法.进一步结合数据滤波技术,研究了多变量方程误差自回归滑动平均系统的子系统梯度迭代辨识方法、部分耦合（子系统）梯度迭代辨识方法、部分耦合子系统最小二乘迭代辨识方法.文中给出了几个典型算法的计算步骤. 相似文献
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为了开展往返平飘式探空组网观测的仿真和模拟,以及评估组网观测对数值天气预报的影响,并实现往返平飘式探空在目标观测中的应用,本文提出了一种基于高分辨率数值天气模式的往返平飘式探空轨迹模拟和预报方法。基于我国自主研发的GRAPES区域高分辨率模式,初步建立了往返平飘式探空的轨迹预报系统。该系统将往返平飘式探空的上升段、平漂段和下降段的轨迹方程,以及下降段降落伞的动力学方程,直接嵌入到高分辨率数值天气模式中,实现对往返平飘式探空轨迹的模拟和预报。利用轨迹预测系统对63个往返平飘式探空轨迹进行轨迹预报试验和评估,试验结果表明,该系统的轨迹预测结果合理可信,6 h的轨迹预报平均误差小于40 km。 相似文献
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三维可压缩大气中的云尺度模式 总被引：33，自引：15，他引：33
我们设计了一个三维云尺度模式,它的控制方程由二部分组成:一是Euler式的可压缩运动方程,连续方程,压力变化方程及热力学方程;二是Lagrange式的云-降水微物理方程组。由于声波的存在对各个方程积分过程的影响程度不同,运用了时间分离方法。网格结构设计了二种:一般的和交叉的,并分别采用了松野积分方案和半隐式积分方案。模式经过严格的调试以后,进行了多个个例模拟研究,表明模式是稳定的,给出了合理的三维对流的发展图象,不仅模拟出垂直对流环流,而且模拟出对应的水平涡坏。利用该模式,研究了水平涡坏的形成和发展对云内下沉气流激发的影响和作用。 相似文献
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THE FORMULATION OF FIDELITY SCHEMES OF PHYSICAL CONSERVATION LAWS AND IMPROVEMENTS ON A TRADITIONAL SPECTRAL MODEL OF BAROCLINIC PRIMITIVE EQUATIONS FOR NUMERICAL PREDICTION* 
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下载免费PDF全文 Zhong Qing 《Acta Meteorologica Sinica》1999,13(2):226-248
In this paper,two formulation theorems of time-difference fidelity schemes for general quadratic and cubic physical conservation laws are respectively constructed and proved,with earlier major conserving time-discretized schemes given as special cases.These two theorems can provide new mathematical basis for solving basic formulation problems of more types of conservative time-discrete fidelity schemes,and even for formulating conservative temporal-spatial discrete fidelity schemes by combining existing instantly conserving space-discretized schemes.Besides.the two theorems can also solve two large categories of problems about linear and nonlinear computational instability.The traditional global spectral-vertical finite-difference semi-implicit model for baroclinic primitive equations is currently used in many countries in the world for operational weather forecast and numerical simulations of general circulation.The present work,however,based on Theorem 2 formulated in this paper,develops and realizes a high-order total energy conserving semi-implicit time-difference fidelity scheme for global spectral-vertical finite-difference model of baroclinic primitive equations.Prior to this,such a basic formulation problem remains unsolved for long,whether in terms of theory or practice.The total energy conserving semi-implicit scheme formulated here is applicable to real data long-term numerical integration.The experiment of thirteen FGGE data 30-day numerical integration indicates that the new type of total energy conserving semi-implicit fidelity scheme can surely modify the systematic deviation of energy and mass conserving of the traditional scheme.It should be particularly noted that,under the experiment conditions of the present work,the systematic errors induced by the violation of physical laws of conservation in the time-discretized process regarding the traditional scheme designs(called type Z errors for short) can contribute up to one-third of the total systematic root-mean-square(RMS) error at the end of second week of the integration and exceed one half of the total amount four weeks afterwards.In contrast,by realizing a total energy conserving semi-implicit fidelity scheme and thereby eliminating corresponding type Z errors,roughly an average of one-fourth of the RMS errors in the traditional forecast cases can be reduced at the end of second week of the integration,and averagely more than one-third reduced at integral time of four weeks afterwards.In addition,experiment results also reveal that,in a sense,the effects of type Z errors are no less great than that of the real topographic forcing of the model.The prospects of the new type of total energy conserving fidelity schemes are very encouraging. 相似文献
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Summary The fourth generation of numerical weather prediction (NWP) models is currently under development at the Deutscher Wetterdienst
(DWD) consisting of a global grid point model (GME) and limited-area Lokal-Modell (LM). The nonhydrostatic fully compressible
LM has been designed to meet high-resol ution regional fore-cast requirements at meso-β and meso-γ scales. The initial LM
implementation is based on the NCAR/Penn State MM5 with the addition of a novel generalized terrain-following coordinate and
rotated lat-lon grid. A fully 3D semi-implicit time-stepping scheme has been implemented by retaining the full buoyancy term
instead of the approximate form found in MM5. In contrast with earlier schemes, mass-lumping is not applied to simplify the
elliptic operator on an Arakawa-C/Lorenz grid. The resulting variable-coefficient elliptic problem is solved using a minimal
residual Krylov iterative method with line relaxation preconditione rs. The new semi-implicit scheme is compared with a variant
of the Klemp–Wilhelmson split-explicit scheme (horizontal explicit, vertical implicit) on the basis of computational efficiency
and accuracy at resolutions ranging from 7 km to 400 m. Both idealized 3D mountain wave flows and naturally occuring flows
are analyzed. Below the tropopause, the 3D semi-implicit scheme can be more efficient for low Mach number M ≪ 1 flows when the number of small time steps Δt
s
of the split-explicit approach increases with the sound-speed Courant number.
Revised October 7, 1999 相似文献
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钟青 《Acta Meteorologica Sinica》1999,(2)
In this paper,two formulation theorems of time-difference fidelity schemes for generalquadratic and cubic physical conservation laws are respectively constructed and proved,with earliermajor conserving time-discretized schemes given as special cases.These two theorems can providenew mathematical basis for solving basic formulation problems of more types of conservative time-discrete fidelity schemes,and even for formulating conservative temporal-spatial discrete fidelityschemes by combining existing instantly conserving space-discretized schemes.Besides.the twotheorems can also solve two large categories of problems about linear and nonlinear computationalinstability.The traditional global spectral-vertical finite-difference semi-implicit model for baroclinicprimitive equations is currently used in many countries in the world for operational weatherforecast and numerical simulations of general circulation.The present work,however,based onTheorem 2 formulated in this paper,develops and realizes a high-order total energy conservingsemi-implicit time-difference fidelity scheme for global spectral-vertical finite-difference model ofbaroclinic primitive equations.Prior to this,such a basic formulation problem remains unsolved forlong,whether in terms of theory or practice.The total energy conserving semi-implicit schemeformulated here is applicable to real data long-term numerical integration.The experiment of thirteen FGGE data 30-day numerical integration indicates that the newtype of total energy conserving semi-implicit fidelity scheme can surely modify the systematicdeviation of energy and mass conserving of the traditional scheme.It should be particularly notedthat,under the experiment conditions of the present work,the systematic errors induced by theviolation of physical laws of conservation in the time-discretized process regarding the traditionalscheme designs(called type Z errors for short)can contribute up to one-third of the totalsystematic root-mean-square(RMS)error at the end of second week of the integration and exceedone half of the total amount four weeks afterwards.In contrast,by realizing a total energyconserving semi-implicit fidelity scheme and thereby eliminating corresponding type Z errors,roughly an average of one-fourth of the RMS errors in the traditional forecast cases can be reducedat the end of second week of the integration,and averagely more than one-third reduced at integraltime of four weeks afterwards.In addition,experiment results also reveal that,in a sense,theeffects of type Z errors are no less great than that of the real topographic forcing of the model.The prospects of the new type of total energy conserving fidelity schemes are very encouraging. 相似文献
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Three-Step Difference Scheme for Solving Nonlinear Time-Evolution Partial Differential Equations 下载免费PDF全文
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
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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
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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
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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