共查询到20条相似文献,搜索用时 15 毫秒
1.
完全非内插半拉格朗日格式在一维
Burgers方程及二维浅水波方程上的应用 总被引:3,自引:2,他引:1
在作者过去提出的完全非内插半拉格朗日格式的基础上,针对半拉格朗日格式由于内插带来预报场人为的光滑性问题,进一步发展了这种计算格式,证明了此格式的计算稳定性。为检验这种新的计算格式的性能,在一维和二维问题上进行了应用。在一维问题中采用了一维无粘Burgers方程(方程中有突变点);二维问题采用了浅水波方程,同时将这些计算结果与Ritchie方案及欧拉方案或一般半拉格朗日内插方案的计算结果进行了比较,发现新格式消除了内插和预报场的人为光滑,并且计算精度有一定程度的提高,这为以后将此格式推广到全球谱模式打下了基础。 相似文献
2.
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
3.
Semi-implicit algorithms are popularly used to deal with the gravitational
term in numerical models. In this paper, we adopt the method of
characteristics to compute the solutions for gravity waves on a sphere
directly using a semi-Lagrangian advection scheme instead of the
semi-implicit method in a shallow water model, to avoid expensive matrix
inversions. Adoption of the semi-Lagrangian scheme renders the numerical
model always stable for any Courant number, and which saves CPU time. To
illustrate the efficiency of the characteristic constrained interpolation
profile (CIP) method, some numerical results are shown for idealized test
cases on a sphere in the Yin-Yang grid system. 相似文献
4.
5.
AN IMPROVED SEMI-IMPLICIT TIME DIFFERENCE SCHEME OF SPECTRAL MODEL AND NUMERICAL APPLICATIONS 总被引:1,自引:0,他引:1
In fact,the popular semi-implicit time difference scheme of spectral model still includes someimportant linear terms using time explicit difference scheme,and the major terms are directlyrelated to fast internal-and external-gravity waves in the atmospheric forecasting equation.Additionally,due to using time difference on two terms at different time.the popular schemeartificially introduces unbalance between pressure gradient force and Coriolis force terms whilenumerically computing their small difference between large quantities.According to thecomputational stability analysis conducted to the linear term time difference scheme in simpleharmonic motion equation,one improved semi-implicit time difference scheme is also designed inour study.By adopting a kind of revised time-explicit-difference scheme to these linear terms thatstill included in spectral model governing equations,the defect of spectral model which only partlyusing semi-implicit integrating scheme can be overcome effectively.Moreover,besides all spectralcoefficients of prognostic equations,especially of Helmholtz divergence equation,can be workedout without any numerical iteration,the time-step (computation stability) can also be enlarged(enhanced) by properly introducing an adjustable coefficient. 相似文献
6.
AN IMPROVED SEMI-IMPLICIT TIME DIFFERENCE SCHEME OF SPECTRAL MODEL AND NUMERICAL APPLICATIONS* 下载免费PDF全文
In fact,the popular semi-implicit time difference scheme of spectral model still includes some important linear terms using time explicit difference scheme,and the major terms are directly related to fast internal-and external-gravity waves in the atmospheric forecasting equation.Additionally,due to using time difference on two terms at different time.the popular schemear tificially introduces unbalance between pressure gradient force and Coriolis force terms while numerically computing their small difference between large quantities.According to the computational stability analysis conducted to the linear term time difference scheme in simple harmonic motion equation,one improved semi-implicit time difference scheme is also designed in our study.By adopting a kind of revised time-explicit-difference scheme to these linear terms that still included in spectral model governing equations,the defect of spectral model which only partlyusing semi-implicit integrating scheme can be overcome effectively.Moreover,besides all spectral coefficients of prognostic equations,especially of Helmholtz divergence equation,can be worked out without any numerical iteration,the time-step (computation stability) can also be enlarged (enhanced) by properly introducing an adjustable coefficient. 相似文献
7.
8.
1.IntroductionWeatherforecastingmodelisasetofpartialdifferentialequations(PDE).Itshouldsatisfycertaininitial--boundaryconditions.Clearly,oneofthemostimportantimprovementsinweatherforecastingmodelistooptimizeitsinitialandboundaryconditions.Forthesimplicityofdiscussion,wemightregardthespatialboundaryconditionasakindofinitialconditioninspatialdimension.Aneffectivedataassimilationprocedureisrequiredinordertoutilizewidelycollectivedatafortheweatherforecastingmodelandfindanoptimalinitialcondition.… 相似文献
9.
PRM标量平流方案在GRAPES全球预报系统中的应用 总被引:4,自引:0,他引:4
如何更好地模拟水物质的分布,对于数值天气预报效果的改进,特别是对于更好地模拟降水过程,具有重要的意义。半拉格朗日模式中的标量平流计算要求做到高精度、守恒、正定和保形,但GRAPES_GFS (Global-Regional Assimilation and PrEdiction System, Global Forecast System) 中采用的QMSL(Quasi-Monotone Semi-Lagrangian)平流方案在水汽的强梯度、不连续区域计算精度较低,且不能做到严格守恒。本研究借鉴计算流体力学领域的研究进展,将一个基于分段有理函数的物质平流方案PRM(Piecewise Rational Method)引入GRAPES_GFS中,按照通量形式求解水汽方程,并对极区进行了混合等技术处理。通过一系列理想试验对两种平流方案进行了对比,证明了PRM方案精度较高,特别是在水汽梯度大的区域优势明显,频散、耗散误差较小,守恒、保形性也要好于QMSL方案。通过对GRAPES_GFS中批量预报试验效果的检验,验证了PRM方案可以有效地改进模式对水物质分布的模拟,提高了降水的预报效果,对模式综合预报性能的提升也有明显作用。 相似文献
10.
GRAPES区域模式水汽平流方案的比较与改进 总被引:7,自引:2,他引:7
与欧拉显式时间差分方法相比,GRAPES区域模式采用半隐半拉格朗日时间差分方案可增加时间步长且不影响稳定性,而且模式积分可有较高的计算效率和准确性。半拉格朗日法需要用到内插算法来预测下一时刻的值,对于水汽场的内插值来说,常常会造成预报值的过饱和或者是负值,需要进行特殊处理。比较GRAPES模式的准单调半拉格朗日方案(QMSL)和高精度正定保形方案(PRM),分析模式的降水预报、形势预报,同时初步总结了两方案的优缺点。在参考LCSL(Linear Constraint Semi-Lagarangain)方案的基础上,改进QMSL方案,通过连续试验运行,表明新方案基本稳定可靠,对于降水预报、形势预报有一定的改进,在台风预报试验中也有良好的表现。 相似文献
11.
12.
A positivity-preserving conservative semi-Lagrangian transport model by multi-moment finite volume method has been developed on the cubed-sphere grid. Two kinds of moments(i.e., point values(PV moment) at cell interfaces and volume integrated average(VIA moment) value) are defined within a single cell. The PV moment is updated by a conventional semi-Lagrangian method, while the VIA moment is cast by the flux form formulation to assure the exact numerical conservation. Different from the spatial approximation used in the CSL2(conservative semi-Lagrangian scheme with second order polynomial function) scheme, a monotonic rational function which can effectively remove non-physical oscillations is reconstructed within a single cell by the PV moments and VIA moment. To achieve exactly positive-definite preserving, two kinds of corrections are made on the original conservative semi-Lagrangian with rational function(CSLR)scheme. The resulting scheme is inherently conservative, non-negative, and allows a Courant number larger than one.Moreover, the spatial reconstruction can be performed within a single cell, which is very efficient and economical for practical implementation. In addition, a dimension-splitting approach coupled with multi-moment finite volume scheme is adopted on cubed-sphere geometry, which benefitsthe implementation of the 1 D CSLR solver with large Courant number.The proposed model is evaluated by several widely used benchmark tests on cubed-sphere geometry. Numerical results show that the proposed transport model can effectively remove nonphysical oscillations and preserve the numerical nonnegativity, and it has the potential to transport the tracers accurately in a real atmospheric model. 相似文献
13.
14.
R. S. Nanjundiah 《Climate Dynamics》2000,16(4):303-317
The impact of numerical modeling of moisture transport on the simulation of the seasonal mean pattern of precipitation in
the tropics is studied. The NCAR CCM2 with spectral and semi-Lagrangian moisture transport has been used for this purpose.
The differences in the numerical modeling of moisture transport are found to have a significant impact on the simulation of
the seasonal mean patterns. The major differences while using the spectral method (vis-a-vis the semi-Lagrangian method) are
(1) a decrease in rainfall over the Indian monsoon region, (2) a decrease in rainfall over the west Pacific region and (3)
an increase in rainfall over the central and east Pacific regions. There are substantial differences in the amount of precipitable
water vapor simulated by the two moisture transport techniques. It is shown that the difference in precipitable water vapor
between the two simulations is associated with changes in the vertical moist static stability (VMS) of the atmosphere, and
differences in the simulated precipitation patterns.
Received: 7 August 1998 / Accepted: 15 October 1999 相似文献
15.
Prof. Z. I. Janjić 《Meteorology and Atmospheric Physics》1995,55(1-2):1-16
Summary Two-time-level multiply-upstream semi-Lagrangian schemes were examined in the case of the self-advecting, one-dimensional nonlinear momentum conservation equation. The shock formation process was analyzed. It is pointed out that the shocks cannot be created in the truncated systems satisfying the Pudykiewicz, Benoit and Staniforth criterion.The numerical integrations were restricted to 12 h. It was shown that, at least in the sub-CFL range, increased complexity of the scheme can compensate reduced horizontal resolution. A considerable sensitivity of the schemes with respect to the time step was detected. In the super-CFL mode, several windows on various time scales were found within which the Pudykiewicz, Benoit and Staniforth criterion was satisfied. The time step of 1.44 times the maximum time step allowed by the CFL criterion was used in the semi-Lagrangian runs.The super-CFL, semi-Lagrangian solutions were diverging progressively from the sub-CFL ones as the forecasts advanced. This was also reflected in the energy spectra.Unacceptably large energy losses were encountered in the super-CFL, semi-Lagrangian runs. Most of these losses could be explained by the reduced mean wind speed, i.e., the amplitude of the zero wavenumber wave. At the same time, the energy content in the shorter waves increased. In a more complex model, such a situation would resemble a loss of zonal, and an increase of transient eddy kinetic energy.A trajectory error measure was defined as the maximum absolute value of the distance between the actual arriving point of the particle originating at the estimated departure point, and the grid point assumed to be the arrival point in the semi-Lagrangian procedure. In contrast to the sub-CFL regime, this measure could reach a considerable fraction of the grid distance in the computations with the super-CFL time steps.In the physical system considered, the trajectories are determined only by the velocities at the departure points. With the semi-Lagrangian schemes the distances traveled by the particles are estimated on the basis of the velocities at the points downstream with respect to the departure points. Thus, unless the solution is smooth (in space and time) on the scales of the extrapolation distances/times, the upstream extrapolation does not promise the convergence of the solution.With 16 Figures 相似文献
16.
长时效的正压原始方程能量完全守恒(拟)谱模式 总被引:4,自引:1,他引:3
遵循误差反演补偿新计算原理,对正压原始方程传统气象全球拟谱模式方案进行了改造,构造了正压原始方程能量完全守恒全球拟增模式新计算方案,解决了正压原始方程的(非线性)计算稳定性问题和能量守恒整体性质保持问题,改进了相应正压原始方程传统气象全球拟谱模式方案的计算效能。新方案的数值试验表明:在计算实践上,新方案在解决能量守恒问题的同时,可解决(非线性)计算稳定性问题,并在一定条件下可解决非线性计算收敛性问题。进一步的比较数值试验还表明:在计算实践上,新方案具有在提高相应传统气象方案的计算精度,减少其计算量的同时,延长其计算时效,解决其中一类特定“气候漂移”问题方面的效用。本工作原理也适用于斜压原始方程情形。 相似文献
17.
A new non-interpolating semi-Lagrangian scheme has been proposed, which can eliminate any interpolation, and consequently numerical smoothing of forecast fields. Here the new scheme is applied to KdV equation and its performance is assessed by comparing the numerical results with those produced by Ritchie’s scheme (1986). The comparison shows that the non-interpolating semi-Lagrangian scheme appears to have efficiency advantages. 相似文献
18.
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
19.
LONG VALID TIME ENERGY PERFECT CONSERVATIVE FIDELITY SPECTRAL SCHEMES OF BAROTROPIC PRIMITIVE EQUATIONS* 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
20.
有效的正压原始方程拟能守恒保真(拟)谱模式 总被引:4,自引:0,他引:4
本工作遵循保真计算原理与方法,对正压原始方程气象传统全球(拟)谱模式方案进行改造,构造了正压原始方程拟能完全守恒(拟)谱模式新型保真计算方案,解决了正压原始方程的(非线性)计算稳定性问题和拟能守恒整体性质保持问题,改进了相应正压原始方程气象传统全球(拟)谱模式方案的计算效能。新型保真方案的数值实验表明,计算实践中,新方案在解决拟能守恒问题的同时,可解决(非线性)计算稳定问题,并在一定条件下可解决非线性计算收敛性问题。进一步的比较数值实验还表明,计算实践中,新型保真计算方案在提高相应气象传统方案的计算精度、 相似文献