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在交错网格上,基于高精度的Gauss积分公式,针对浅水波方程设计了对模拟涌波具有高分辨率的完全二阶精度的数值计算格式。由于采用了交错网格,差分格式不需要解Riemann问题,因此本文格式具有计算简单、工作量少、编程简便等特点。另外,在一维单个方程时,本文格式在CFL(Courant Friedrich Lewy)条件限制下为TVD(Total Variation Diminishing)格式,在二维和三维情况下格式具有MmB(Maximum and Minimum Bounds Preserving)性质。利用国家高性能计算中心(合肥)的曙光1000型分布存储大规模并行机,对在交错网格下所构造的求解浅水方程的高分辨差分格式进行了并行实现,几个算例的计算结果令人满意。 相似文献
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建立了一种在非规则结构化网格上求解平面二维浅水流动的有限体积方法。通过采用地形在离散网格内双线性变化及离散网格界面间地形连续的地形逼近方法和应用可以有效处理间断问题的Roe格式来离散浅水方程中的对流项,并通过VanLeer提出的状态插值法提高格式精度。在计算原始变量在网格内的插值梯度时,采用最小二乘方法求变量的最优梯度代替差分计算梯度,从而可采用任意形状的不规则四边形网格离散计算域。计算实例表明,该方法能够计算间断问题并能够处理各种复杂流态的过渡,具有较好适应性和计算精度,能够满足不同实际问题的计算要求。 相似文献
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基于有限体积方法和结构化网格,建立了海底滑坡引起的波浪传播数值模型。模型控制方程为考虑了海床随时间变化的二维浅水方程。采用中心迎风格式计算控制体界面数值通量,采用线性重构技术、局部海床高程处理技术和全隐式离散底摩阻项,保证了格式的和谐性、守恒性和水深非负性,有效处理了海岸动边界问题。时间积分采用具有强稳定性质的二阶龙格-库塔方法(ssp RK)。针对滑坡体兴波经典算例开展数值模拟,将计算结果与解析解、实验结果及其他模型计算结果进行比较和分析。结果表明,对于所考虑的计算工况,模型能较合理地模拟滑坡兴波的产生、传播和爬高过程。 相似文献
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为保证计算格式的和谐性,通过特殊的底坡源项处理技术,在三角形网格上建立了求解二维浅水流动方程的具有空间二阶精度的Godunov格式。应用准确Riemann解求解法向数值通量,用改正的干底Riemann解处理动边界问题。经典型算例和钱塘江河口涌潮计算验证,表明模型健全,分辨率高,具有较大的推广应用价值。 相似文献
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复杂边界下的流场数值模拟常基于非结构化网格进行求解,建立一种在非结构混合网格上求解水深平均的二维浅水方程的模型,以便精确模拟复杂边界、提高计算效率。该模型时间项离散采用隐格式使得模型具有较好的稳定性,对流项和扩散项分别采用总变差减小(Total Variation Diminishing,TVD)格式和构造辅助点的方法来离散,同时采用水深平均的标准k-ε模型来封闭湍流模型。选用两个经典验证算例检验模型,计算结果表明,基于非结构混合网格开发的模型具有较高的精度,且收敛性能较好。 相似文献
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二维分数阶对流-弥散方程的数值解 总被引:1,自引:0,他引:1
对二维时间分数阶对流-弥散方程和二维空间分数阶对流-弥散方程分别建立了差分格式,实现了对其的数值求解。针对理想算例进行计算求解,分析了时间和空间分数阶阶数取不同值时的扩散变化规律,验证了各自所描述的时间相关性与空间相关性。同时与传统的二维整数阶对流-弥散方程的求解结果作了对比。当时间和空间分数阶阶数α与γ分别取整数时,二维时间分数阶对流-弥散方程和二维空间分数阶对流-弥散方程都与传统二维整数阶对流-弥散方程的计算结果相同,说明提出的对二维分数阶对流-弥散方程的数值求解方法是可行的。其结果对地下水溶质运移的进一步研究提供了有效的手段。 相似文献
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为了选择适用于复杂连续弯道的二次流修正方法,选取了线性方法中两种典型的计算模式,通过在正交曲线坐标系二维浅水动量方程中增加扩散应力项开发了考虑二次流影响的平面二维水流模型。基于不同复杂度的4个连续弯道试验的水位和流速分布资料,通过理论分析和数值试验对比定量评估了传统二维模型和两种二次流修正方法在连续弯道水流模拟中的效果。测试结果表明,Delft3D模型的二次流修正方法自由度较高,适用于不同复杂度的连续弯道水流模拟,而Lien模型二次流修正方法适用于微弯或中弯,应用于中弯时需要慎重选用,不适用于急弯连续弯道模拟。两种方法比较,建议连续弯道水流模拟中优选Delft3D模型的二次流修正方法。 相似文献
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A coupled 2D mathematical modelling study of landslide dam failure and flood is presented, complementing our experimental
investigation presented in the companion paper. The model is built upon the shallow water hydrodynamic equations. The governing
equations are numerically solved using the total-variation-diminishing version of the second-order weighted-average-flux method
along with the HLLC (Harten, Lax and van Leer with Contact wave restored) approximate Riemann solver. Two parameters related
to bed-load sediment transport and critical slope stability are calibrated using the measured stage hydrographs from two runs
of the flume experiments. The calibrated model is then applied to other independent runs of the experiments featuring different
inflow discharges, dam geometry, dam composition and initial breach dimensions. It is found to be able to satisfactorily reproduce
the measured stage hydrographs and the widening of initial breach. The experimental observation of the prime role of the inflow
discharge and initial breach in dictating the dam failure process and flood is unequivocally resolved, along with the impacts
of dam geometry as well the content of cohesive clay and gravel in the dam. Interestingly, the downstream peak discharge and
stage of the flood are substantially reduced by initial breach, which clearly exemplifies its role in modulating the flooding. 相似文献
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Thida Pongsanguansin Montri Maleewong Khamron Mekchay 《Computational Geosciences》2016,20(6):1269-1285
A well-balanced finite volume method for solving two-dimensional shallow water equations with weighted average flux (WAF) is developed in this work to simulate flooding. Friction source terms are estimated with a semi-implicit scheme resulting in an efficient numerical method for simulating shallow water flows over irregular domains, for both wet and dry beds. A wet/dry cell tracking technique is also presented for reducing computational time. The accuracy of these methods are investigated by application to well-studied cases. For practical purposes, the developed scheme is applied to simulate the flooding of the Chao Phraya river from Chai Nat to Sing Buri provinces in Thailand during October 13–17, 2011. The numerical simulations yield results that agree with the existing data obtained from the satellite images. 相似文献
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Lucio Di Matteo Cristina Pauselli Daniela Valigi Maurizio Ercoli Mauro Rossi Giacomo Guerra Costanza Cambi Remo Ricco Giuseppe Vinti 《Landslides》2018,15(1):173-180
Shallow landslide failures are distributed worldwide and cause economic losses and fatalities. A proper evaluation of the possible occurrence of shallow landslides requires reliable characterization of water content. Volumetric water content (θ) is commonly estimated using dielectric sensors, which use manufacturers’ calibration curves developed for specific soil types. In this study, we present the experimental results achieved during a laboratory calibration of a capacitance probe (PR2/6 probe), tested on two sandy soils widely outcropping in Central Italy. The proposed equations demonstrate a more reliable estimation of θ with respect to the generalized soil equation provided by the manufacturer, which overestimates θ by up to 10 percentage points. Such overestimation could affect the evaluation of suction stress in partially saturated shallow soils affecting the slope stability analysis. Although the use of θ from correct calibration equations provides less precautionary factor of safety values, a reliable evaluation of the soil moisture condition is fundamental when mapping and predicting the spatial and temporal occurrence of shallow landslides. The use of the PR2/6 probe with the appropriate soil calibration equations in early warning monitoring systems will provide a more reliable forecast, minimizing the number of false alarms. 相似文献
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Comparison of linear and nonlinear shallow wave water equations applied to tsunami waves over the China Sea 总被引:4,自引:0,他引:4
Yingchun Liu Yaolin Shi David A. Yuen Erik O. D. Sevre Xiaoru Yuan Hui Lin Xing 《Acta Geotechnica》2009,4(2):129-137
This paper discusses the applications of linear and nonlinear shallow water wave equations in practical tsunami simulations.
We verify which hydrodynamic theory would be most appropriate for different ocean depths. The linear and nonlinear shallow
water wave equations in describing tsunami wave propagation are compared for the China Sea. There is a critical zone between
400 and 500 m depth for employing linear and nonlinear models. Furthermore, the bottom frictional term exerts a noticeable
influence on the propagation of the nonlinear waves in shallow water. We also apply different models based on these characteristics
for forecasting potential seismogenic tsunamis along the Chinese coast. Our results indicate that tsunami waves can be modeled
with linear theory with enough accuracy in South China Sea, but the nonlinear terms should not be neglected in the eastern
China Sea region. 相似文献
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重点分析了研究区潜水、浅层承压水、泉水及地表水δD、δ18O的分布特征, 并对5组水文钻探井地下水样品进行分析. 潜水δD变化范围为-97.32‰~-67.51‰, 平均值为-80.34‰; δ18O为-15.85‰~-10.66‰, 平均值为-12.08‰. 浅层承压水δD为-111.93‰~-68.38‰, 平均值为-84.79‰; δ18O为-16.01‰~-10.52‰, 平均值为-12.30‰. 泉水δD为-102.06‰~-71.63‰, 平均值为-84.10‰; δ18O为-14.21‰~-9.70‰, 平均值为-12.24‰. 地表水δD为-90.53‰~-60.99‰, 平均值为-72.58‰; δ18O在-13.20‰~-9.54‰, 平均值为-11.21‰. 地下水δ13C为-9.4‰~-5.6‰, 平均值为-8.3‰, 极差为3.8‰. 结果表明: 地下水与地表水均起源于当地大气降水. 潜水与浅层承压水水力联系较强, 潜水与浅层承压水属于同一含水系统. 与浅层承压水相比, 深层承压水年龄较大, 在20 ka左右, 属于沉积埋藏水. 深层承压水与浅层承压水的水力联系较弱. 潜水与浅层承压水的δ13C值较为接近, 且接近大气CO2的δ13C值-7‰. 研究区地下水中碳的主要来源为大气CO2. 相似文献