A temporally second-order accurate Godunov-type scheme for solving the extended Boussinesq equations     

J.B. Shiach  C.G. Mingham 《Coastal Engineering》2009

A numerical scheme for solving the class of extended Boussinesq equations is presented. Unlike previous schemes, where the governing equations are integrated through time using a fourth-order method, a second-order Godunov-type scheme is used thus saving storage and computational resources. The spatial derivatives are discretised using a combination of finite-volume and finite-difference methods. A fourth-order MUSCL reconstruction technique is used to compute the values at the cell interfaces for use in the local Riemann problems, whilst the bed source and dispersion terms are discretised using centred finite-differences of up to fourth-order accuracy. Numerical results show that the class of extended Boussinesq equations can be accurately solved without the need for a fourth-order time discretisation, thus improving the computational speed of Boussinesq-type numerical models. The numerical scheme has been applied to model a number of standard test cases for the extended Boussinesq equations and comparisons made to physical wave flume experiments.  相似文献   

双三次数值模式与理想Lamb波、龙卷扰动对比模拟分析     

辜旭赞  张兵 《气象科技》2007,35(5):613-620

通过"双三次曲面拟合—时间步长积分—双三次曲面拟合……",实现成为一种双三次曲面拟合新算法数值模式。它对模式大气作非线性(空间二阶可导)描述,是用数值分析(三次样条/双三次曲面)与计算方法近似求解大气运动非线性偏微分方程组。用Z坐标系高分辨率双三次数值模式,采用原始大气运动方程组和采用欧拉时间积分方案,设置理想扰动,对大气声波Lamb波做数值模拟;采用大气不可压假定,除去声波,对大气重力波龙卷扰动做数值模拟。对比模拟发现:理想Lamb波以声速在水平方向传播,扰动能量频散快,仅能在原地持续数秒钟;理想龙卷扰动则在原地可持续约1 min,且波动内圈(外圈)自下至上始终处于风场辐合(辐散)状态,具冷心结构和气压驻波特征,可因水汽进入扰动与借助凝结潜热释放而得到发展。  相似文献   

菏泽市紫外线辐射变化特征及月预报方程     

孙翠凤  ;窦坤  ;程德海  ;李瑛  ;吴雷柱 《干旱气象》2014,(4):677-682

利用2008年4月至2012年12月菏泽市紫外线观测资料以及地面常规气象观测资料和空气质量资料,分析了该地区太阳紫外线辐射的变化特征及其与各因子的相关关系,并建立逐月预报方程。结果表明:菏泽紫外线辐射年总量达到187.98 W/m2,春夏两季明显高于秋冬两季,5月达到全年的最大值,1月为全年的最小值;3~9月紫外线辐射极大值均可达到5级,其他月份均可达到4级。不同天气条件下紫外线辐射强度存在明显差异,其中晴天紫外线辐射强且稳定,呈抛物线变化;多云天紫外线辐射波动较大,时强时弱;阴天紫外线辐射相对较弱。紫外线辐射强度与风速、能见度、气温呈正相关,与总云量、低云量、相对湿度呈负相关,与SO2、PM10、NO2、PM2.5多呈负相关。基于多元线性回归分析向后剔除变量方法得出的逐月预报方程,经检验总体预报效果较好,对当地紫外线等级预报工作具有参考意义。  相似文献   

Internal solitary waves shoaling onto a shelf: Comparisons of weakly-nonlinear and fully nonlinear models for hyperbolic-tangent stratifications     

《Ocean Modelling》2014

In this study the evolution of internal solitary waves shoaling onto a shelf is considered. The results of high resolution two-dimensional numerical simulations of the incompressible Euler equations are compared with the predictions of several weakly-nonlinear shoaling models of the Korteweg–de Vries family including the Gardner equation and the cubic regularized long wave (or Benjamin–Bona–Mahoney) equation. Wave models in both physical x–t space and in s–x space are considered where s is a commonly used characteristic time variable. The effects of rotation, background currents and damping are ignored. The Boussinesq and rigid lid approximations are also used. The shoaling internal solitary waves generally fission into several waves. Reflected waves are negligible in the cases considered here. Several hyperbolic tangent stratifications are considered with and without a critical point. Among the equations in x–t space the cubic regularized long wave equation gives the best predictions. The Gardner equation in s–x space gives the best predictions of the shape of the leading waves on the shelf, but for many stratifications it predicts a propagation speed that is too large.  相似文献   

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仲崇豪  姚宜斌  刘强  张良 《大地测量与地球动力学》2014,34(4):153-156

?????????????С???????????????????????С???????????????С???????????????????????????????????????С?????????????????????????С??????????????????й?????????????????????????y?????????  相似文献   

裂缝诱导双相HTI介质模型及其弹性波传播方程   总被引：1，自引：0，他引：1  

高炜  刘财  郭智奇  兰慧田  黄航 《世界地质》2014,33(4):904-933

将Biot双相介质理论与Gurevich裂缝各向异性理论相结合,建立了能够同时考虑实际裂缝性储层孔隙性和各向异性的裂缝诱导双相HTI介质模型。从本构方程、动力学方程和动力学达西定律出发,推导出了裂缝诱导双相HTI介质中弹性波传播的一阶速度-应力方程,并针对方程的刚性问题,给出了利用显式二阶时间积分法数值求解该方程时所需要满足的稳定性条件。该方程能够定量地给出双相HTI介质的波场特征与裂缝参数、背景孔隙介质参数之间的关系,描述弹性波在这种介质中的传播机理。  相似文献   

双时间步法在二维浅水方程求解中的应用          下载免费PDF全文

喻海军  黄国如  武传号 《水科学进展》2014,25(4):542-549

针对传统算法效率低的问题,将隐式双时间步法应用于求解二维浅水方程,建立了非结构网格下高效的有限体积模型。在应用双时间步法时,虚拟时间层中的定常问题采用高效的隐式LU-SGS（Lower-Upper Symmetric Gauss-Seidel）方法进行迭代求解。通过模拟计算4个典型算例以及与传统显式算法进行比较,对模型精度、效率及处理实际问题能力进行检验,分析了时间步长、内迭代次数对模型性能的影响。结果表明,双时间步法放宽了稳定性对时间步长的限制,时间步长可取到显式格式10倍以上,计算耗时减少了50%以上,模型具有良好精度与适应性,具有较好的推广应用价值。  相似文献   

测距定位方程非线性平差的封闭牛顿迭代公式     

薛树强  杨元喜  党亚民 《测绘学报》2014,43(8):771-777

测距方程;非线性强度;最小二乘;高斯-牛顿法;牛顿法;病态方程  相似文献   

Deterministic non-linear wave prediction using probe data     

E. Blondel  F. Bonnefoy  P. Ferrant 《Ocean Engineering》2010,37(10):913-926

The accurate prediction of non-linear sea states represents a great challenge, with a number of applications in oceanography, marine engineering, security of people and marine transportation, etc. In this paper, we report on the development of two efficient deterministic prediction models for 2D irregular wave-fields. These models are based on the exploitation of wave elevation time series given by one or more probes and on the use of two different numerical models for the wave-fields simulation. Two effective data assimilation processes are developed to improve the wave-field estimates obtained from the study of one or several probe signals, so that we obtain proper initial conditions for the forecast. The assimilation schemes have been validated on the reconstruction of model-generated observations and accurate predictions of the corresponding synthetic wave-fields evolution have been obtained.  相似文献   

The tripole: A new coherent vortex structure of incompressible two-dimensional flows     

Lorenzo M. Polvani  Xavier J. Carton 《地球物理与天体物理流体动力学》2013,107(1-4):87-102

Abstract

Using a contour dynamical algorithm, we have found rotating tripolar V-state solutions for the inviscid Euler equations in two-dimensions. We have studied their geometry as a function of their physical parameters. Their stability was investigated with the aid of contour surgery, and most of the states were found to be stable. Under finite-amplitude perturbations, tripoles are shown to either fission into two asymmetric dipoles or to evolve into a shielded axisymmetric vortex, demonstrating the existence of two new ‘‘reversible transitions'’ between topologically distinct coherent vortex structures. These dynamical results are confirmed by pseudo-spectral simulations, with which we also show how continuous tripolar long-lived coherent vortex structures can be generated in a variety of ways.  相似文献