Horizontal solute transport from a pulse type source along temporally and spatially dependent flow: Analytical solution

Yadav, Sanjay; Kumar, Abhishek; Kumar, Naveen

doi:10.1016/j.jhydrol.2011.02.024

Cited by 31 publications

(11 citation statements)

References 31 publications

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“…Three main terminologies, including scale‐dependent , non‐Fickian and pre‐asymptotic , have been proposed to describe properties of pollutant transport in heterogeneous media deviating from Fickian transport in ideal, homogeneous media (note that the concept of ‘anomalous transport’ was also widely used by hydrologists, but we did not use it here since it has no strict definition in physics and it overlaps with the three terminologies mentioned above). For example, conservative solute moving in heterogeneous porous media was found to be scale‐dependent , characterized by the apparent dispersion coefficient D or dispersivity α increasing with the travel distance or time (Dagan, 1989; Gelhar, Welty, & Rehfeldt, 1992; Gelhar, 1993; Sousa, de Oliveira, Machado, & Carvalho, 2020; Wang et al, 2018; Yadav & Kumar, 2019; among many others). This property is likely driven by the spatial variability of hydraulic conductivity ( K ), motivating various approximations of macrodispersion (e.g., the asymptotic longitudinal dispersivity) using the statistics of ln K (Dagan, 1982, 1988; Gelhar, 1993; Gelhar & Axness, 1983; Hess, Wolf, & Celia, 1992; Neuman, Winter, & Newman, 1987).…”

Section: Introductionmentioning

confidence: 99%

Nonlocal transport models for capturing solute transport in one‐dimensional sand columns: Model review, applicability, limitations and improvement

Zhang

Zhou

Yin

et al. 2020

Hydrological Processes

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Modelling pollutant transport in water is one of the core tasks of computational hydrology, and various physical models including especially the widely used nonlocal transport models have been developed and applied in the last three decades. No studies, however, have been conducted to systematically assess the applicability, limitations and improvement of these nonlocal transport models. To fill this knowledge gap, this study reviewed, tested and improved the state-of-the-art nonlocal transport models, including their physical background, mathematical formula and especially the capability to quantify conservative tracers moving in one-dimensional sand columns, which represents perhaps the simplest real-world application. Applications showed that, surprisingly, neither the popular time-nonlocal transport models (including the multi-rate mass transfer model, the continuous time random walk framework and the time fractional advection-dispersion equation), nor the spatiotemporally nonlocal transport model (ST-fADE) can accurately fit passive tracers moving through a 15-m-long heterogeneous sand column documented in literature, if a constant dispersion coefficient or dispersivity is used. This is because pollutant transport in heterogeneous media can be scale-dependent (represented by a dispersion coefficient or dispersivity increasing with spatiotemporal scales), non-Fickian (where plume variance increases nonlinearly in time) and/or pre-asymptotic (with transition between non-Fickian and Fickian transport). These different properties cannot be simultaneously and accurately modelled by any of the transport models reviewed by this study. To bypass this limitation, five possible corrections were proposed, and two of them were tested successfully, including a time fractional and space Hausdorff fractal model which minimizes the scaledependency of the dispersion coefficient in the non-Euclidean space, and a two-region time fractional advection-dispersion equation which accounts for the spatial mixing of solute particles from different mobile domains. Therefore, more efforts are still needed to accurately model transport in non-ideal porous media, and the five model corrections proposed by this study may shed light on these indispensable modelling efforts.

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Section: Introductionmentioning

confidence: 99%

Nonlocal transport models for capturing solute transport in one‐dimensional sand columns: Model review, applicability, limitations and improvement

Zhang

Zhou

Yin

et al. 2020

Hydrological Processes

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“…The literature [10] was the first to propose a fuzzy algorithm for image enhancement, which is the first algorithm to apply fuzzy sets to the field of image enhancement, and many researchers have joined the study because of the novelty of the algorithm. The literature [11] proposed an edge enhancement algorithm with the help of fuzzy theory to obtain the image feature values, and the method is good for enhancing the image detail information. The literature [12] proposed a fuzzy contrast enhancement algorithm that adapts the local contrast for image enhancement.…”

Section: Related Studiesmentioning

confidence: 99%

Fractional-Order Adaptive $P$ -Laplace Equation-Based Art Image Edge Detection

Chen

2021

Advances in Mathematical Physics

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In recent years, with the rapid development of image processing research, the study of nonstandard images has gradually become a research hotspot, for example, fabric images, remote sensing images, and gear images. Some of the remote sensing images have a complex background and low illumination compared with standard images and are easy to be mixed with noise during acquisition; some of the fabric images have rich texture information, which adds difficulty to the related processing, and are also easy to be mixed with noise during acquisition. In this paper, we propose a fractional-order adaptive P -Laplace equation image edge detection algorithm for the problem of image edge detection in which the edge and texture information of the image is lost. The algorithm can apply for the order adaptively to filter the noise according to the noise distribution of the image, and the adaptive diffusion factor is determined by both the fractional-order curvature and fractional-order gradient of the iso-illumination line and combined with the iterative approach to realize the fine-tuning of the noisy image. The experimental results demonstrate that the algorithm can remove the noise while preserving the texture and details of the image. A fractional-order partial differential equation image edge detection model with a fractional-order fidelity term is proposed for Gaussian noise. The model incorporates a fractional-order fidelity term because this fidelity term smoothes out the rougher parts of the image while preserving the texture in the original image in greater detail and eliminating the step effect produced by other models such as the Perona-Malik (PM) and Rudin-Osher-Fatemi (ROF) models. By comparing with other algorithms, the image edge detection effect is measured with the help of evaluation metrics such as peak signal-to-noise ratio and structural similarity, and the optimal value is selected iteratively so that the image with the best edge detection result is retained. A convolutional mask image edge detection model based on adaptive fractional-order calculus is proposed for the scattered noise in medical images. The adaption is mainly reflected in the model algorithm by constructing an exponential parameter relation that is closely related to the image, which can dynamically adjust the parameter values, thus making the model algorithm more practical. The model achieves the scattering noise removal in four steps.

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“…The mediums through which the solute transport occurs are homogeneous (when the dispersivity does not depend to the position) or heterogeneous (when the dispersivity is a distance dependent function). This characteristic of a medium as an important role to the solute transport trough them (Kumar and Yadav, 2014;Sanskrityayn et al, 2018;Yadav and Kumar, 2019). The advection-dispersion equation can be solved numerically or analytically.…”

Section: Introductionmentioning

confidence: 99%

Analytical Solution of 1D Advection-Dispersion Equation In Finite Groundwater Reservoir With Spatially Dependent Dispersivity And Two Inputs Sources With Source-Sink Term Impact

Tjock-Mbaga

Abiama

Ema’a

et al. 2021

Preprint

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This study derives an analytical solution of a one-dimensional (1D) advection-dispersion equation (ADE) for solute transport with two contaminant sources that takes into account the source term. For a heterogeneous medium, groundwater velocity is considered as a linear function while the dispersion as a nth-power of linear function of space and analytical solutions are obtained for and . The solution in a heterogeneous finite domain with unsteady coefficients is obtained using the Generalized Integral Transform Technique (GITT) with a new regular Sturm-Liouville Problem (SLP). The solutions are validated with the numerical solutions obtained using MATLAB pedpe solver and the existing solution from the proposed solutions. We exanimated the influence of the source term, the heterogeneity parameters and the unsteady coefficient on the solute concentration distribution. The results show that the source term produces a solute build-up while the heterogeneity level decreases the concentration level in the medium. As an illustration, model predictions are used to estimate the time histories of the radiological doses of uranium at diﬀerent distances from the sources boundary in order to understand the potential radiological impact on the general public.

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Horizontal solute transport from a pulse type source along temporally and spatially dependent flow: Analytical solution

Cited by 31 publications

References 31 publications

Nonlocal transport models for capturing solute transport in one‐dimensional sand columns: Model review, applicability, limitations and improvement

Nonlocal transport models for capturing solute transport in one‐dimensional sand columns: Model review, applicability, limitations and improvement

Fractional-Order Adaptive $P$ -Laplace Equation-Based Art Image Edge Detection

Analytical Solution of 1D Advection-Dispersion Equation In Finite Groundwater Reservoir With Spatially Dependent Dispersivity And Two Inputs Sources With Source-Sink Term Impact

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Horizontal solute transport from a pulse type source along temporally and spatially dependent flow: Analytical solution

Cited by 31 publications

References 31 publications

Nonlocal transport models for capturing solute transport in one‐dimensional sand columns: Model review, applicability, limitations and improvement

Nonlocal transport models for capturing solute transport in one‐dimensional sand columns: Model review, applicability, limitations and improvement

Fractional-Order Adaptive P -Laplace Equation-Based Art Image Edge Detection

Analytical Solution of 1D Advection-Dispersion Equation In Finite Groundwater Reservoir With Spatially Dependent Dispersivity And Two Inputs Sources With Source-Sink Term Impact

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Product

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Fractional-Order Adaptive $P$ -Laplace Equation-Based Art Image Edge Detection