An efficient space-fractional dispersion approximation for stream solute transport modeling     

Chaopeng Shen  Mantha S. Phanikumar 《Advances in water resources》2009

The success of transient storage (TS) modeling for natural streams depends, in part, on the ability to describe the dispersion process accurately. Evidence based on stream tracer data shows that solute transport processes often do not follow the classical second-order dispersion model (e.g., early breakthrough and faster than Fickian travel times were observed). While models based on space-fractional dispersion are a promising alternative, different definitions of fractional derivatives exist in the literature. Unlike integer-order derivatives, fractional derivatives represent convolutions of concentration with long-range spatial correlation and numerical approximations can produce dense matrices. Therefore issues of both accuracy and computational efficiency need to be examined to successfully identify model parameters for natural streams. In this paper, we first compare the performance of several numerical approaches for solving the space-fractional dispersion equation. We examine three different numerical approaches to approximate the space-fractional derivatives including: (a) a fully-implicit scheme based on the shifted Grünwald–Letnikov (GL) approximation (b) a three-point implicit representation based on the GL formula and (c) a three-point implicit scheme based on mass conservation and the Caputo definition of the fractional derivative. We then use an operator-splitting technique to evaluate a TS model based on space-fractional dispersion (the FSTS model) and test the model against analytical solutions and stream tracer data. A sequence acceleration method (Richardson extrapolation) significantly improves the performance of all schemes examined. Results indicate that the fully-implicit GL method with Richardson extrapolation produces the most accurate solutions while the three-point implicit GL scheme has a stringent time-step restriction to produce acceptable solutions. The three-point implicit scheme based on the Caputo derivative produces accurate solutions in a fraction of the time taken by the fully-implicit GL method and represents the best trade-off between accuracy and computational efficiency for practical applications. The scheme is suitable for parameter estimation and is used to successfully describe tracer data in a natural stream.  相似文献   

A meshless method to simulate solute transport in heterogeneous porous media     

Paulo A. Herrera  Marco Massabó  Roger D. Beckie 《Advances in water resources》2009

We derive a meshless numerical method based on smoothed particle hydrodynamics (SPH) for the simulation of conservative solute transport in heterogeneous geological formations. We demonstrate that the new proposed scheme is stable, accurate, and conserves global mass. We evaluate the performance of the proposed method versus other popular numerical methods for the simulation of one- and two-dimensional dispersion and two-dimensional advective–dispersive solute transport in heterogeneous porous media under different Pèclet numbers. The results of those benchmarks demonstrate that the proposed scheme has important advantages over other standard methods because of its natural ability to control numerical dispersion and other numerical artifacts. More importantly, while the numerical dispersion affecting traditional numerical methods creates artificial mixing and dilution, the new scheme provides numerical solutions that are “physically correct”, greatly reducing these artifacts.  相似文献   

Comparison of numerical simulation of solute transport with observed experimental data in a silt loam subsoil   总被引：1，自引：0，他引：1  

A. I. Paseka  M. Z. Iqbal  J. C. Walters 《Environmental Geology》2000,39(9):977-989

 Solute transport experiments were conducted on loamy soils of north-eastern Iowa, USA, and the results were compared with a numerical solution of a classical advection-dispersion transport model developed in this study. Flow experiments in the laboratory on undisturbed soil columns showed a flow rate of water much higher than was estimated from the soil properties and grain-size analysis data, suggesting preferential flow regime in the soil. In contrast, the relative concentration peaks of Cl^– and Br^– in the effluent were only approximately 70% of those predicted by the classical advection-dispersion equation (ADE). In addition, the experimental breakthrough curves (BTCs) showed greater tailings of these ions than the model solution. These observations suggest a loss of solute mass during transport from the dynamic flowing regions to a stagnant, immobile water phase in the soil matrix. Experiments in small disturbed soil columns showed that movement of Cl^– and Br^– is in good agreement with predictions of the classical ADE when the tracers are applied as a continuous source. However, in the case of a pulse source, the BTCs of Cl^– and Br^– matched the model only in the ascending part of the curves. Such variation indicates greater retardation of these ions than that of simulation, probably caused by the decrease in soil permeability due to cation exchange reactions in the soil involving monovalent and divalent cation pairs such as K⁺–Ca²⁺ and K⁺–Mg²⁺. In addition, retardation occurred as a result of the continuous saturation of soil columns which seemed to have caused an expansion of clay minerals, thus resulting in decreased soil permeability. In both the continuous and the pulse-source experiments, K⁺ was not detected in the effluent samples, which seemed to have been lost in exchange reactions and adsorption. Received: 20 November 1998 · Accepted: 19 July 1999  相似文献   

孔隙地层轻质水泥套管井中偶极弯曲波的激发与传播特性          下载免费PDF全文

吴洋  吕伟国  杨蒙恩  崔志文  刘金霞  王克协 《地球物理学报》2020,63(6):2488-2496

针对软地层套管井中弯曲波频散移向高频,以致超出了现行偶极声波测井仪器的激发频带的问题,本文在井外为孔隙地层时,采用Biot模型对套管井多极源激发的声波场进行了理论推导,对套管井偶极弯曲波的频散特性进行了数值模拟,考察了高密度水泥(或快速水泥)和低密度水泥(或轻质水泥)情况下的弯曲波频散,分析了不同水泥环对弯曲波主频散区和激发谱偏移的影响,重点对轻质水泥套管井中偶极源激发的模式波频散与激发谱及临界折射P、S波激发特性进行了研究,并考察了渗透率、孔隙度对弯曲波频散及衰减的影响,利用实轴积分法计算了偶极声源激发的时域全波波形.分析对比结果表明,在快速水泥情况下弯曲波频散曲线随着地层特征横波速度的减小会迅速向高频移动,随着快速水泥向轻质水泥变化,弯曲波频散曲线向高频移动将会减缓,对于特征横波速度低于1400m·s~(-1)的软地层,偶极弯曲波基础模式主频散区(或截止频率)可以由原来13kHz向低频移动至4kHz;在轻质水泥套管井中,无论是硬地层还是软地层,在目前偶极声波测井仪器声源主频激发下,接收波形中弯曲波均占主导地位.  相似文献   

Effect of stress interactions on anisotropic P-SV-wave dispersion and attenuation for closely spaced cracks in saturated porous media     

Chenghao Cao  Fangyuan Chen  Li-Yun Fu  Jing Ba  Tongcheng Han 《Geophysical Prospecting》2020,68(8):2536-2556

Generally, local stress induced by individual crack hardly disturbs their neighbours for small crack densities, which, however, could not be neglected as the crack density increases. The disturbance becomes rather complex in saturated porous rocks due to the wave-induced diffusion of fluid pressures. The problem is addressed in this study by the comparison of two solutions: the analytical solution without stress interactions and the numerical method with stress interactions. The resultant difference of effective properties can be used to estimate the effect of stress interactions quantitatively. Numerical experiments demonstrate that the spatial distribution pattern of cracks strongly affects stress interactions. For regularly distributed cracks, the resulting stress interaction (shielding or amplification) shows strong anisotropy, depending on the arrangement and density of cracks. It has an important role in the estimation of effective anisotropic parameters as well as the incident-angle-dependency of P- and SV-wave velocities. Contrarily, randomly distributed cracks with a relative small crack density generally lead to a strong cancellation of stress interactions across cracks, where both the numerical and analytical solutions show a good agreement for the estimation of effective parameters. However, for a higher crack density, the incomplete cancellation of stress interactions is expected, exhibiting an incidence-angle dependency, slightly affecting effective parameters, and differentiating the numerical and analytical solutions.  相似文献   

Multi-scale analysis for transport of fine settling particles through an ice-covered channel in a laminar flow condition     

《国际泥沙研究》2022,37(6):794-808

The current research deals with the dispersion of fine settling particles in a fluid flowing through an ice-covered channel under the laminar flow condition. An analytical solution of the two-dimensional convection–diffusion equation, based on the multi-scale homogenization technique, is obtained. To validate the current study, analytical results for the dispersion coefficient are compared with the available earlier research work. Moreover, the proposed analytical solutions for mean concentration distributions of the tracers are compared with the numerical results obtained from the finite difference technique. From the industrial and environmental points of view, the vertical concentration distribution provides a very significant information. The downstream evolution of the concentration distribution also is shown for typical time periods at different values of the settling velocity. The approach to the vertical uniformity shows that it is too slow a process in comparison to that of longitudinal normality. It was found that settling velocities of particles disturb the vertical uniformity and the centroid of the solute cloud rises due to the increase in settling velocity. Results illustrate that in the downstream direction, the vertical concentration distribution increases near the bed surface and it decreases in the proximity of the ice-covered surface of the channel with the increase of settling velocity, but the mean concentration of the solute increases. The current study may play an important role to understand the mechanism of the sedimentation process in a closed channel system.  相似文献   

唐山北部地区浅层一维剪切波速度结构初步研究     

王莉婵  毛国良  蔡玲玲  马旭东  王亚玲  王宁 《震灾防御技术》2022,17(1):104-113

2019年8月2日河北省唐山市路南区某矿井区发生M_L2.4巷道塌陷,基于塌陷周边台站观测到的短周期瑞雷波,提取面波基阶群速度频散曲线,并利用迭代反演方法得到研究区域地下10 km深度范围内的一维剪切波速度结构,用于精定位分析。速度分析结果表明,研究区域浅表剪切波速度约为2.46 km/s;深度为2 km时,塌陷周边存在小范围的低速区,速度约为2.57 km/s;深度约为4 km时,剪切波速度达3.47 km/s;深度为5～9 km时,唐山东部沉积盆地内存在1个剪切波低速层。精定位分析结果表明,增加浅层速度模型有助于提高深度较小的地震定位精度;塌陷周边的低速区向下延伸近20 km,为地震多发区。  相似文献   

放射性核素大气弥散模式研究综述   总被引：4，自引：0，他引：4       下载免费PDF全文

刘爱华  蒯琳萍 《气象与环境学报》2011,27(4):59-65

放射性核素大气弥散模式可以模拟正常工况和事故工况下,放射性核素在不同尺度下的大气输送与扩散,为核电站选址、辐射环境监测和核事故应急提供科学依据。归纳了目前广泛用于模拟核素大气弥散的各种模式,介绍了这些模式的研究进展和适用范围。结果表明：对于区域范围小于2 km的弥散,一般可采用CFD（Computational flu...  相似文献   

华北地区勒夫波噪声层析成像研究   总被引：17，自引：2，他引：15       下载免费PDF全文

房立华  吴建平  王未来  王长在  杨婷 《地球物理学报》2013,56(7):2268-2279

利用华北地震科学台阵200个流动地震台站、14个月的连续波形数据,通过互相关方法提取了勒夫波的经验格林函数,使用多重滤波方法测量了5229条勒夫波的群速度频散曲线,采用噪声层析成像方法得到了研究区域4~30 s的勒夫波群速度分布图像,横向分辨率在多数区域可以达到0.25°×0.25°. 层析成像结果显示,短周期的群速度分布特征与地表地质和构造特征基本一致,华北盆地和山西断陷带内的盆地呈现低速异常,燕山隆起和太行山隆起表现为高速异常;中周期的群速度分布图揭示了华北盆地内部隆起和坳陷的空间分布范围及沉积层的厚度差异. 勒夫波频散曲线具有明显的分区特征,太行山隆起、燕山隆起和鄂尔多斯块体东北缘的频散曲线形态基本一致,和其它典型克拉通相似;张渤地震带和山西裂谷盆地的频散曲线基本一致,接近于埃塞俄比亚裂谷. 中西部块体的平均频散曲线和其它典型克拉通相似,而东部块体的频散曲线和中西部块体存在较大差异,且低于其它典型克拉通,表明东部块体的地壳受到了强烈的破坏和改造,而中西部块体受改造的程度较低,仍具有稳定克拉通的物理性质. 太行山重力梯度带的东西两侧在地形地貌、速度结构、频散特征、地壳厚度、岩石圈厚度以及地幔过渡带厚度均存在显著差异,是划分华北克拉通破坏空间范围的一条重要界线,推测华北克拉通的破坏范围主要在太行山重力梯度带以东.  相似文献   

用于声波方程数值模拟的时间-空间域有限差分系数确定新方法   总被引：4，自引：4，他引：0       下载免费PDF全文

梁文全  杨长春  王彦飞  刘红伟 《地球物理学报》2013,56(10):3497-3506

声波方程数值模拟已广泛应用于理论地震计算,同时构成了地震逆时偏移成像技术的基础.对于有限差分法而言,在满足一定的稳定性条件时,普遍存在着因网格化而形成的数值频散效应.如何有效地缓解或压制数值频散是有限差分方法研究的关键所在.为精确求解空间偏导数,相继发展了高阶差分格式优化方法和伪谱方法.近期,为更好地缓解数值频散,提出了时间-空间域有限差分方法,该方法采用了泰勒展开近似方法来确定有限差分格式系数,因而只能保证在一定的小范围内很好的拟合波场传播规律.为进一步压制数值频散效应,本文引入了时间-空间域特定波数点满足频散关系的方法,根据震源、波速和网格间距确定波数范围,同时考虑了多个传播角度,然后建立方程确定了相应的有限差分格式系数,使得差分系数能在更大范围符合波场传播规律.通过频散分析和正演模拟,验证了本文方法的有效性.  相似文献