共查询到18条相似文献，搜索用时 93 毫秒
1.
The relationship between nonconservative schemes and initial values of nonlinear evolution equations 总被引：1，自引：0，他引：1
LIN Wantao 《大气科学进展》2004,21(2):277-282
For the nonconservative schemes of the nonlinear evolution equations, taking the one-dimensionalshallow water wave equation as an example, the necessary conditions of computational stability are given.Based on numerical tests, the relationship between the nonlinear computational stability and the construc-tion of difference schemes, as well as the form of initial values, is further discussed. It is proved throughboth theoretical analysis and numerical tests that if the construction of difference schemes is definite, thecomputational stability of nonconservative schemes is decided by the form of initial values. 相似文献
2.
The Impacts of Initial Perturbations on the Computational Stability of Nonlinear Evolution Equations 
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下载免费PDF全文 The impacts of initial perturbations on the computational stability of nonlinear evolution equations for non-conservative difference schemes and non-periodic boundary conditions are studied through theoretical analysis and numerical experiments for the case of onedimensional equations.The sensitivity of the difference scheme to initial values is further analyzed.The results show that the computational stability primarily depends on the form of the initial values if the difference scheme and boundary conditions are determined.Thus,the computational stability is sensitive to the initial perturbations. 相似文献
3.
LONG VALID TIME ENERGY PERFECT CONSERVATIVE FIDELITY SPECTRAL SCHEMES OF BAROTROPIC PRIMITIVE EQUATIONS 下载免费PDF全文
下载免费PDF全文 钟青 《Acta Meteorologica Sinica》1995,(3)
In accordance with a new compensation principle of discrete computations,the traditional meteo-rological global (pseudo-) spectral schemes of barotropic primitive equation (s) are transformed intoperfect energy conservative fidelity schemes,thus resolving the problems of both nonlinear computa-tional instability and incomplete energy conservation,and raising the computational efficiency of thetraditional schemes.As the numerical tests of the new schemes demonstrate,in solving the problem of energy conser-vation in operational computations,the new schemes can eliminate the (nonlinear) computational in-stability and,to some extent even the (nonlinear) computational diverging as found in the traditionalschemes,Further contrasts between new and traditional schemes also indicate that,in discrete opera-tional computations,the new scheme in the case of nondivergence is capable of prolonging the valid in-tegral time of the corresponding traditional scheme,and eliminating certain kind of systematical com-putational“climate drift”,meanwhile increasing its computational accuracy and reducing its amount ofcomputation.The working principle of this paper is also applicable to the problem concerning baroclin-ic primitive equations. 相似文献
4.
By using the symmetric equations of atmospheric dynamics in y-z plane with vertical and horizontal shear of wind, the nonlinear ordinary differential equation is derived with the method of travelling wave.Its stability is discussed by using the theory of nonlinear stability and the KDV equation is solved. The effects of linear CISK, nonlinear CISK, inertial stability and vertical shear of wind on the amplitude and the width of isolated inertial gravitational wave are discussed. In order to understand deeply the formation and development of meso-scale synoptic systems, such as the squall line, MCC, the cold surge of Asia high and typhoon, the factors of development of the isolated inertial gravity wave are analysed. 相似文献
5.
Although incorporating the horizontal diffusion into the atmospheric governing equations is apart of the dynamics of a model,it is based on the computational consideration originally,which isto overcome the nonlinear aliasing or computational instability and smooth the physical fields at thesame time.The generally used forms of the fourth-order diffusion,either linear or nonlinear,however,can not properly describe the real physical diffusion processes and thus affect theaccuracy of forecasting and modeling.In this paper,based on the nature of the physical diffusion.the scheme of horizontal diffusion of the MM5 Version 3 is improved according to the second law ofthermodynamics which controls the irreversable evolutionary direction of a many-body system andthe potential ability of the improvement of the new scheme in modeling accuracy is revealed byintroducing the technique suggested in this paper,via a theoretical case and the computational caseof the hurricane Andrew that landed on Florida in 1992. 相似文献
6.
The introduction of “hydrostatic extraction” scheme, or “standard stratification approximation”, into spectral model gained some advantages compared with commonly used schemes. However, computational instability may oc-cur for high vertical resolution versions if the stratification parameter C0 taken as a constant. In this paper, the pos-sible cause leading to the instability is discussed and an improved scheme presented where C0 is generalized to be a function of both height and latitudes. Hence the reference atmosphere gets closer to the real atmosphere and the tem-perature deviation field to be expanded becomes smoother everywhere. Test by real case forecasts shows good computational stability of the new scheme and better prediction performance than usual schemes of spectral model. 相似文献
7.
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
8.
In this paper, the coupling schemes of atmosphere-ocean climate models are discussed with one-dimensional advection equations. The convergence and stability for synchronous and asynchronous schemes are demonstrated and compared.Conclusions inferred from the analysis are given below. The synchronous scheme as well as the asynchronous-implicit scheme in this model are stable for arbitrary integrating time intervals. The asynchronous explicit scheme is unstable under certain conditions, which depend upon advection velocities and heat exchange parameters in the atmosphere and oceans. With both synchronous and asynchronous stable schemes the discrete solutions converge to their unique exact ones. Advections in the atmosphere and ocean accelerate the rate of convergence of the asynchronous-implicit scheme. It is suggusted that the asynchronous-implicit coupling scheme is a stable and efficient method for most climatic simulations. 相似文献
9.
Baroclinic Instability in the Generalized Phillips’ Model Part II: Three-layer Model 总被引：2，自引：0，他引：2
The nonlinear stability of the three-layer generalized Phillips model, for which the velocity in each layer is constant and the top and bottom surfaces are either rigid or free, is studied by employing Arnol’d’s variational principle and a prior estimate method. The nonlinear stability criteria are established. For com-parison, the linear instability criteria are also obtained by using normal mode method, and the influences of the free parameter, β parameter and curvature in vertical profile of the horizontal velocity on the linear in-stability are discussed by use of the growth rate curves.The comparison between the nonlinear stability criterion and the linear one is made. It is shown that in some cases the two criteria are exactly the same in form, but in other cases, they are different. This phenom-enon, which reveals the nonlinear property of the linear instability features, is explained by the explosive resonant interaction (ERI). When there exists the ERI, i.e., the nonlinear mechanisms play a leading role in the dynamical system, the nonlinear stability criterion is different from the linear one; on the other hand, when there does not exist the ERI, the nonlinear stability criterion is the same as the linear one in form. 相似文献
10.
Numerical simulation of typhoon surges along the east coast of Zhejiang and Jiangsu Provinces 总被引：2，自引：0，他引：2
Using conventional two-dimensional nonlinear storm model, the storm surges caused by the six ty-phoons with different kinds of tracks which hit the coast of Zhejiang and Jiangsu Provinces including Shanghai during the period from 1953 to 1974 are computed numerically. To avoid the nonlinear and linear computational instabilities, a finite-difference scheme with the quadratic conservation (or the semi-momentum) is adopted and a criterion for linear computational stability is derived. The basic parameters used in this computation are: the space step Δs=30km, the time step Δt=200sec, the coefficient of the wind stress = 2.6 "10-> and the coefficient of the bottom friction v&2=2.0x 10-'. The pressure and surface wind distribution for typhoon are assumed to be characterized by Fujita's pressure formula and Uerto's wind model, respectively. 相似文献
11.
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
12.
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
13.
针对非线性发展方程的非守恒格式,以一维浅水波方程为例,对非守恒格式的计算稳定性进行了研究分析,探讨了非线性发展方程的非守恒格式与初值的关系.理论分析和数值试验表明,在格式结构已经确定的情况下,非守恒格式的计算稳定性主要由初值的形式所决定. 相似文献
14.
LONG VALID TIME ENERGY PERFECT CONSERVATIVE FIDELITY SPECTRAL SCHEMES OF BAROTROPIC PRIMITIVE EQUATIONS* 下载免费PDF全文
下载免费PDF全文 Zhong Qing 《Acta Meteorologica Sinica》1995,9(3):313-324
In accordance with a new compensation principle of discrete computations,the traditional meteorological global (pseudo-) spectral schemes of barotropic primitive equation (s) are transformed into perfect energy conservative fidelity schemes,thus resolving the problems of both nonlinear computational instability and incomplete energy conservation,and raising the computational efficiency of the traditional schemes.As the numerical tests of the new schemes demonstrate,in solving the problem of energy conservation in operational computations,the new schemes can eliminate the (nonlinear) computational instability and,to some extent even the (nonlinear) computational diverging as found in the traditional schemes,Further contrasts between new and traditional schemes also indicate that,in discrete operational computations,the new scheme in the case of nondivergence is capable of prolonging the valid in-tegral time of the corresponding traditional scheme,and eliminating certain kind of systematical computational "climate drift",meanwhile increasing its computational accuracy and reducing its amount of computation.The working principle of this paper is also applicable to the problem concerning baroclinic primitive equations. 相似文献
15.
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
16.
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
17.
大气动力学方程组的定性理论及其应用 总被引：9，自引：2，他引：7
基于完整的湿大气动力学方程组,利用无穷维动力系统的新理论和新方法,系统讨论了强迫耗散的非线性大气系统的定性理论及其应用。将完整的强迫耗散非线性湿大气动力学方程组化为Hilbert空间中一个等价的算子方程,研究了算子的性质及其物理意义,在此基础上得到湿大气系统全局吸引子的存在性定理,揭示出系统向外源的非线性适应特征,并把结果推广到有地形动力作用和非定常外源强迫的情形。同时探讨了大气方程组惯性流形的存在,大气多平衡态产生的根源以及强迫、耗散和非线性对系统解的渐近行为的影响。在理论结果的基础上,提出强迫耗散的非线性动力系统中存在三类时间边界层、方程组简化准则、分解算法的算子约束原则以及支撑吸引子基底的少数自由度的构造方法,探讨了理论在非线性发展方程差分格式的设计和计算稳定性分析、多平衡态的数值分析、数值模式延伸预报的改进、短期气候预测以及一类中尺度系统分析与预测中的应用,指出描述长期过程动力学模式的必备条件,给出初值与模式相协调的合理解释。最后,对今后的研究方向作了展望。 相似文献