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1.
This paper proposes a new two—step non—oscillatory shape—preserving positive definite finite difference advection transport
scheme, which merges the advantages of small dispersion error in the simple first-order upstream scheme and small dissipation
error in the simple second-order Lax-Wendroff scheme and is completely different from most of present positive definite advection
schemes which are based on revising the upstream scheme results. The proposed scheme is much less time consuming than present
shape—preserving or non-oscillatory advection transport schemes and produces results which are comparable to the results obtained
from the present more complicated schemes. Elementary tests are also presented to examine the behavior of the scheme.
This work is supported by the Ntional Natural Science Foundation of China. 相似文献
2.
Summary Four numerical methods suitable for the calculation of transport are compared on a linear two-dimensional advection equation. It is found that a mass-compensation algorithm which removes negative values has also a beneficial effect on the accuracy of schemes which are of higher order but are not positive. It is shown by numerical experiments, that the upstream spline advection scheme combined with a mass compensation is prefereable for some applications rather than other high accurate positive schemes like the flux-corrected transport scheme.With 3 Figures 相似文献
3.
利用中尺度模式ＭＭ４，研究了中尺度模式的暴雨模拟对于不同不汽输送方案的敏感性。采用５种平流差分格式来计算水汽的水平输送，用该模式对３次暴雨过程作了数值试验。并把不同方案的降水模拟结果与实况进行了对比。结果表明，中尺度模式的暴雨模拟对水汽输送方案十分敏感，正定高精度的Ｐｒａｔｈｅｒ格式的模拟结果最接近实况。 相似文献
4.
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
5.
本文在Smolarkiewicz(1983)方案的基础上,提出了一种新的正定平流方案。它是无条件计算稳定的,形式简单、物理意义清楚且阻尼小,能够很容易地应用到多维模式中。文中通过一简单的平流试验,与其它几种有名的正定平流方案进行了比较;最后将这种方案应用到国家气象中心细网格有限区域业务预报模式水汽预报方程中,避免了原水汽计算方案产生严重负水汽的问题,并对24h降水预报场进行分析。 相似文献
6.
Summary The paper concerns the sensitivity of the regional mesoscale model (MM4) to a moisture transport algorithm with different accuracies, and the effective improvement of the capability to simulate meso-scale synoptical event by using the revised version of the algorithm. The two advective schemes of second-order moment conservational Prather scheme (PRS hereinafter) and the polynomial-fitted fourth-order Bott scheme and the upstream scheme (UPS) are introduced into the MM4 to calculate moisture transport in order to provide other types of the algorithm with different accuracies for choice in addition to the original B grid second-order central scheme. Of the three schemes, the first two ensure the positive definite character with high accuracy (almost no numerical disspation and computational dispersion); and the last one also keeps the positive definite feature, but possesses stronger capability of numerical dissipation. Case studies have been undertaken of several rainstorm and typhoon events by virtue of the different-accuracy moisture transport algorithm, other things being the same. Results reveal great differences between them. An significant improvement is found in determining meso-scale synoptic system structure, rain cluster activity, rainstorm belt and its center, severity and its persistence, and the false alarm of or failure to report subrainstorm center when the PRS scheme is employed. Obviously, these differences and improvement are only due to moisture re-distribution for different schemes of moisture transport and the related variation of latent heat. The paper investigates the influences of different numerical schemes. The high accuracy and positive solution PRS application which produces a significant improvement in the model result, demonstrating the sensitivity of the model to moisture distribution in the model represents an important measure to improve the simulation by means of revising the numerically calculating method.With 11 Figures 相似文献
7.
Summary The Euler equations govern the behavior of a fluid in motion. They have long been used as a test-bed for assessing the accuracy and efficiency of numerical schemes for solving them. This study focused on advection dominated flows so all other terms in the equations are omitted. The study examined only explicit schemes and does not address the many alternative approaches such as semi-Lagrangian and implicit formulations. The schemes examined here were applied to test cases of increasing complexity as it is well-known that a particular scheme may work very well on some test problems but fail on others. To avoid such problems, we began with the standard tests such as the advection of sine waves and various other one-dimensional shapes, then moved on to two-dimensional problems and finally tested cases that have many scales.Summarizing, the results from the range of test cases, it was found that the schemes that perform best are high-order upwind schemes, with diminishing returns above fifth- and sixth-order.Finally, the schemes were applied to cases where scalar advection requires that constraints such as positive-definiteness be satisfied. For these problems, the Flux Corrected Transport (FCT) and weighted essentially non-oscillatory (WENO) schemes were also applied. Similar conclusions were drawn, namely, that fifth- and sixth-order FCT and WENO schemes produced excellent simulations. However, these schemes were more computationally expensive than the standard high-order upwind and centred schemes. 相似文献
8.
9.
The radon transport test, which is a widely used test case for atmospheric transport models, is carried out to evaluate the tracer advection schemes in the Grid-Point Atmospheric Model of IAP-LASG （GAMIL）. Two of the three available schemes in the model are found to be associated with significant biases in the polar regions and in the upper part of the atmosphere, which implies potentially large errors in the simulation of ozone-like tracers. Theoretical analyses show that inconsistency exists between the advection schemes and the discrete continuity equation in the dynamical core of GAMIL and consequently leads to spurious sources and sinks in the tracer transport equation. The impact of this type of inconsistency is demonstrated by idealized tests and identified as the cause of the aforementioned biases. Other potential effects of this inconsistency are also discussed. Results of this study provide some hints for choosing suitable advection schemes in the GAMIL model. At least for the polax-region-concentrated atmospheric components and the closely correlated chemical species, the Flux-Form Semi-Lagrangian advection scheme produces more reasonable simulations of the large-scale transport processes without significantly increasing the computational expense. 相似文献
10.
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
11.
分析了新一代非静力中尺度数值模式中常用的三阶龙格-库塔时间分裂显式算法(RK3)的稳定性和误差性质,特别是分析了空间中央差分和迎风偏斜两种不同情况下该算法不同的稳定性和误差性质。运用数学软件先进的符号计算功能,分析了该算法涉及的复杂高阶、高次幂振幅矩阵的特征值性质;并通过一维线性声波-平流方程组的数值模拟实验,检验了时间分裂算法的模拟效果。对振幅矩阵特征值模的表达式进行高阶的级数展开,得到了该算法的分裂误差项的公式;而且,由于特征值模的公式保留了较高阶项,可以同时分析迎风偏斜和中央差两种空间差分格式的分裂误差性质。根据分裂误差项公式,定量地比较了三阶和二阶龙格-库塔格式(RK2)的分裂误差大小以及误差与小时间步数的关系,发现迎风格式RK3的分裂误差明显小于RK2的误差,并具有更好的稳定性质。空间中央差格式的分裂误差项具有更高阶数,比迎风格式具有更小的时间分裂误差。对于各种不同波长的特征值分析和采用中央差格式的数值模拟,也进一步证实空间差分采用中央差时,RK3时间分裂显式算法在不同方向传播的声波振幅几乎没有差别。另外,误差公式以及数值试验结果说明RK3的分裂误差也略小于Adams-Bashforth-Moulton分裂显式法的分裂误差。 相似文献
12.
Application of a Shape-Preserving Advection Scheme to the Moisture Equation in an E-grid Regional Forecast Model 总被引：20，自引：1，他引：20
This paper presents a methodology which is very useful to design shape-preserving advection finite difference scheme on general E-grid horizontal arrangement of variables through introducing a two-step shape-preserving positive definite advection scheme in the moisture equation of the LASG-REM (LASG regional E-grid eta-coordinate forecast model). By trial-forecasting six local heavy raincases, the efficiency of the shape-preserving advection scheme in practical application has been examined. The LASG-REM with the shape-preserving advection scheme has a good forecasting ability for local precipitation. 相似文献
13.
The dependence of results from coarse-resolution models of the North Atlantic circulation on the numerical advection algorithm is studied. In particular, the sensitivity of parameters relevant for climate simulations as e.g., meridional transport of mass and heat and main thermocline thickness is investigated. Three algorithms were considered: (a) a central difference scheme with constant values for horizontal and vertical diffusion, (b) an upstream scheme with no explicit diffusion, and (c) a flux-corrected transport (FCT) scheme with constant and strictly isopycnal diffusion. The temporal evolution of the three models on time scales of centuries is markedly different, the upstream scheme resulting in much shorter adjustment time whereas the central difference scheme is slower and controlled by vertical diffusion rather than advection. In the steady state, the main thermocline structure is much less diffusive in the FCT calculation which also has much lower heat transport. Both horizontal circulation and overturning in the meridional-vertical plane are strongest in the upstream-model. The results are discussed in terms of the effective vertical (diapycnal) mixing in the different models. A significant increase in vertical resolution would be required to eliminate the high sensitivity due to the numerical algorithms, and allow physically motivated mixing formulations to become effective.This paper was presented at the International Conference on Modelling of Global Climate Change and Variability, held in Hamburg 11–15 September 1989 under the auspices of the Meteorological Institute of the University of Hamburg and the Max Planck Institute for Meteorology. Guest Editor for these papers is Dr. L. Dümenil 相似文献
14.
An improved two-time-level split-explicit integration scheme for non-hydrostatic compressible models
A. Gassmann 《Meteorology and Atmospheric Physics》2005,88(1-2):23-38
Summary A new two-time-level split-explicit time integration scheme for the use in non-hydrostatic compressible modelling is presented. It is demonstrated that the scheme is numerically stable and has a smaller splitting error than other comparable split-explicit schemes. This error is due to the combination of advection and fast-wave terms in the numerical scheme.To outline where the splitting error occurs and how it acts within the splitting mechanism, a short review of existing split-explicit time integration methods is given. An in-depth analysis of the eigenvalues of several two-time-level schemes is performed showing that instabilities are associated with the splitting error term. The term has different signs for forward moving and backward moving waves, causing exponential growing or decaying. This unwanted characteristic is not prevented by a diffusive term in general, but might be counteracted by schemes using an estimate of the fast waves at the midpoint of the time increment.The importance of this fast-waves midpoint estimate leads to the formulation of a class of split-explicit two-time-level schemes. Within this framework any forward-in-time and stable advection scheme might be combined with the fast-waves terms in the splitting algorithm.The new method is implemented in the non-hydrostatic model LM of DWD. Some test cases are presented, indicating that the new scheme has the potential to be used in an operational environment. 相似文献
15.
We compare the results of a local and a nonlocal scheme for vertical diffusion in the atmospheric boundary layer with observations at the 200 m tower at Cabauw. This is done for a 12 h period during daytime on 31 May 1978, which is characterised by strong insolation, clear skies, moderately strong winds and weak advection. The local diffusion scheme uses an eddy diffusivity determined independently at each point along the vertical based on local vertical gradients of wind and virtual potential temperature, similar to the usual approach in atmospheric models. The nonlocal scheme determines an eddy diffusivity profile based on a diagnosed boundary-layer height and a turbulent velocity scale. It also incorporates nonlocal (vertical) transport effects for heat and moisture. The boundary-layer diffusion schemes are forced with the locally observed fluxes for heat and moisture. The outputs of the scheme are compared with the observed mean structure along the Cabauw tower, and the radiosonde profile at a nearby location (De Bilt). Overall, the nonlocal scheme transports moisture away from the surface more rapidly than the local scheme, and deposits the moisture at higher levels. The local scheme tends to saturate the lowest model levels unrealistically in comparison with the observations. We also compare the outputs of the two diffusion schemes with the results of a transilient model simulation. Subsequently, we study the impact on the model behaviour by varying important parameters in both diffusion schemes and we investigate the sensitivity to uncertainty in the environmental conditions. Finally, we study the interaction of the diffusion schemes with a simple surface flux scheme. 相似文献
16.
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
17.
18.
不同边界层参数化方案对江苏地区一次平流雾过程的模拟影响 总被引：4，自引：1，他引：3
边界层参数化方案的选取在平流雾的预报准确度上起着决定性的作用。本文利用WRF模式对2013年3月18~19日发生在江苏地区的一次平流雾过程进行数值模拟试验,对耦合不同闭合方式边界层参数化方案的试验结果与实测气象数据进行对比分析,评估了他们对此次平流雾的模拟效果,探讨了边界层高度对此次平流雾的生成和发展的影响。研究结果表明:（1）耦合不同边界层方案的WRF模式对地面气象要素的模拟结果均呈现气温偏低、湿度和风速偏大的特征。（2）QNSE方案对气温的模拟能力最强;ACM2方案对相对湿度的模拟性能最好;YSU方案对风速的模拟效果最佳。不同边界层方案的模拟结果在垂直方向上的差别主要表现在低空相对湿度上:QNSE方案预报的湿度更大。（3）综合TS（Threat Score）和BS（Bias Score）两个评分指标来看,ACM2方案对雾区分布的模拟效果最好。三个边界层方案对此次平流雾的模拟结果在江苏沿海站点的预报评分较高,在距海较远站点的预报评分表现较差。YSU方案对东南沿海地区的雾区预报评分较高;QNSE方案对长江沿江区域的雾区预报评分较高;ACM2方案对沿海地区、尤其对沿海北部地区的有较好的预报效果。（4）QNSE方案对此次平流雾的生成时间、出现地点预报比较准确。（5）平流雾的生成与发展阶段模拟雾区覆盖范围与边界层高度关系十分紧密,适当强度的湍流混合作用有助于平流雾在地面的生成与发展;但是过强的湍流混合作用会导致大雾过早的消散。 相似文献
19.
在凝华增长过程中,冰晶的形状随着温度和湿度的改变而改变,准确模拟冰晶粒子的演变对于提高云模式的模拟能力起着非常重要的作用。在现有的云模式中,冰晶形状通常假设为球形,而在实际大气中,冰晶形状十分复杂。本研究中,我们根据冰晶凝华增长理论模型建立了一个单个冰晶粒子增长模型,模拟了温度分别为-1℃~-30℃时,单个典型非球形冰晶粒子的凝华增长过程。与风洞观测数据相对比,该模型能够抓住单个冰晶粒子的轴长,质量以及纵横比随温度和湿度的变化过程。我们进一步将该理论增长模型应用到群粒子的凝华增长过程的模拟。我们釆用欧拉二维正定平流输送法(MPDATA)模拟了典型非球形冰晶群粒子的凝华增长,并对比分析了在不同纵横比分辨率下的模拟效果以及温度变化对冰晶形状的影响,结果表明运用该数值方法可以合理地模拟出群粒子在凝华增长过程中纵横比的演变。与目前采用的拉格朗日-欧拉混合平流算法比较,该算法能够耦合到欧拉动力框架下的分档云模式中去,这对我们研究冰晶粒子形状对云微物理过程和动力过程的影响,以及它们对冰粒子凝华增长的反馈作用具有非常重要的科学意义。 相似文献
20.
An Eulerian flux-form advection scheme, called the Two-step Shape-Preserving Advection Scheme(TSPAS), was generalized and implemented on a spherical icosahedral hexagonal grid(also referred to as a geodesic grid) to solve the transport equation. The C grid discretization was used for the spatial discretization. To implement TSPAS on an unstructured grid,the original finite-difference scheme was further generalized. The two-step integration utilizes a combination of two separate schemes(a low-order monotone scheme and a high-order scheme that typically cannot ensure monotonicity) to calculate the fluxes at the cell walls(one scheme corresponds to one cell wall). The choice between these two schemes for each edge depends on a pre-updated scalar value using slightly increased fluxes. After the determination of an appropriate scheme, the final integration at a target cell is achieved by summing the fluxes that are computed by the different schemes. The conservative and shape-preserving properties of the generalized scheme are demonstrated. Numerical experiments are conducted at several horizontal resolutions. TSPAS is compared with the Flux Corrected Transport(FCT) approach to demonstrate the differences between the two methods, and several transport tests are performed to examine the accuracy, efficiency and robustness of the two schemes. 相似文献