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Relevant bibliographies by topics / Fractional advection-dispersion equation

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Academic literature on the topic 'Fractional advection-dispersion equation'

Author: Grafiati

Published: 4 June 2021

Last updated: 26 January 2023

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Journal articles on the topic "Fractional advection-dispersion equation"

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Liu, F., V. V. Anh, I. Turner, and P. Zhuang. "Time fractional advection-dispersion equation." Journal of Applied Mathematics and Computing 13, no. 1-2 (2003): 233–45. http://dx.doi.org/10.1007/bf02936089.

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Aljahdaly, Noufe H., Rasool Shah, Muhammed Naeem, and Mohammad Asif Arefin. "A Comparative Analysis of Fractional Space-Time Advection-Dispersion Equation via Semi-Analytical Methods." Journal of Function Spaces 2022 (July 13, 2022): 1–11. http://dx.doi.org/10.1155/2022/4856002.

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The approximate solutions of the time fractional advection-dispersion equation are presented in this article. The nonlocal nature of solute movement and the nonuniformity of fluid flow velocity in the advection-dispersion process lead to the formation of a heterogeneous system, which can be modeled using a fractional advection-dispersion equation, which generalizes the classical advection-dispersion equation and replaces the time derivative with the fractional Caputo derivative. Researchers use a variety of numerical techniques to study such fractional models, but the nonlocality of the deriva

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Khasambiev, Mokhammad Vakhaevich. "Boundary value problemfor multidimensional fractional advection-dispersion equation." Vestnik MGSU, no. 5 (May 2015): 35–43. http://dx.doi.org/10.22227/1997-0935.2015.5.35-43.

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In recent time there is a very great interest in the study of differential equations of fractional order, in which the unknown function is under the symbol of fractional derivative. It is due to the development of the theory of fractional integro-differential theory and application of it in different fields.The fractional integrals and derivatives of fractional integro-differential equations are widely used in modern investigations of theoretical physics, mechanics, and applied mathematics. The fractional calculus is a very powerful tool for describing physical systems, which have a memory and

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Deng, Zhi-Qiang, Vijay P. Singh, and Lars Bengtsson. "Numerical Solution of Fractional Advection-Dispersion Equation." Journal of Hydraulic Engineering 130, no. 5 (2004): 422–31. http://dx.doi.org/10.1061/(asce)0733-9429(2004)130:5(422).

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Benson, David A., Stephen W. Wheatcraft, and Mark M. Meerschaert. "Application of a fractional advection-dispersion equation." Water Resources Research 36, no. 6 (2000): 1403–12. http://dx.doi.org/10.1029/2000wr900031.

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Parsaie, Abbas, and Amir Hamzeh Haghiabi. "Numerical routing of tracer concentrations in rivers with stagnant zones." Water Supply 17, no. 3 (2016): 825–34. http://dx.doi.org/10.2166/ws.2016.175.

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Modeling pollution transmission in rivers is an important subject in environmental engineering studies. Numerical approaches to modeling pollution transmission in rivers are useful tools for managing the water quality. The advection-dispersion equation is the governing equation in the transport of pollution in rivers. Recently, due to advances in fractional calculus in engineering modeling, the simulation of pollution transmission in rivers has been improved using the fractional derivative approach. In this study, by solving the fractional advection-dispersion equation (FRADE), a numerical mod

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Singh, Jagdev, Aydin Secer, Ram Swroop, and Devendra Kumar. "A reliable analytical approach for a fractional model of advection-dispersion equation." Nonlinear Engineering 8, no. 1 (2019): 107–16. http://dx.doi.org/10.1515/nleng-2018-0027.

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Abstract Empirical investigations of solute fate and carrying in streams and rivers often contain inventive liberate of solutes at an upstream perimeter for a finite interval of time. An analysis of various worth references on surface-water-grade mathematical formulation reveals that the logical solution to the continual-parameter advection- dispersion problem for this type of boundary state has been generally missed. In this work, we study the q-fractional homotopy analysis transform method (q-FHATM) to find the analytical and approximate solutions of space-time arbitrary order advection-disp

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Schumer, Rina, David A. Benson, Mark M. Meerschaert, and Stephen W. Wheatcraft. "Eulerian derivation of the fractional advection–dispersion equation." Journal of Contaminant Hydrology 48, no. 1-2 (2001): 69–88. http://dx.doi.org/10.1016/s0169-7722(00)00170-4.

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Jiang, Wei, and Yingzhen Lin. "Approximate solution of the fractional advection–dispersion equation." Computer Physics Communications 181, no. 3 (2010): 557–61. http://dx.doi.org/10.1016/j.cpc.2009.11.004.

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Moradi, G., and B. Mehdinejadiani. "Modelling solute transport in homogeneous and heterogeneous porous media using spatial fractional advection-dispersion equation." Soil and Water Research 13, No. 1 (2018): 18–28. http://dx.doi.org/10.17221/245/2016-swr.

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This paper compared the abilities of advection-dispersion equation (ADE) and spatial fractional advection-dispersion equation (sFADE) to describe the migration of a non-reactive contaminant in homogeneous and heterogeneous soils. To this end, laboratory tests were conducted in a sandbox sizing 2.5 × 0.1 × 0.6 m (length × width × height). After performing a parametric sensitivity analysis, parameters of sFADE and ADE were individually estimated using the inverse problem method at each distance. The dependency of estimated parameters on distance was examined. The estimated parameters at 30 cm we

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Dissertations / Theses on the topic "Fractional advection-dispersion equation"

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Kisela, Tomáš. "Zlomkové diferenciální rovnice a jejich aplikace." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2008. http://www.nusl.cz/ntk/nusl-227885.

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Zlomkový kalkulus je matematická disciplína zabývající se vlastnostmi derivací a integrálů neceločíselných řádů (nazývaných zlomkové derivace a integrály, zkráceně diferintegrály) a metodami řešení diferenciálních rovnic obsahujících zlomkové derivace neznámé funkce (tzv. zlomkovými diferenciálními rovnicemi). V této práci představujeme standardní přístupy k definicím zlomkového kalkulu a důkazy některých základních vlastností diferintegrálů. Dále uvádíme krátký přehled metod řešení některých lineárních zlomkových diferenciálních rovnic a vymezujeme hranice jejich použitelnosti. Na závěr si vš

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Hejazi, Hala Ahmad. "Finite volume methods for simulating anomalous transport." Thesis, Queensland University of Technology, 2015. https://eprints.qut.edu.au/81751/1/Hala%20Ahmad_Hejazi_Thesis.pdf.

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In this thesis a new approach for solving a certain class of anomalous diffusion equations was developed. The theory and algorithms arising from this work will pave the way for more efficient and more accurate solutions of these equations, with applications to science, health and industry. The method of finite volumes was applied to discretise the spatial derivatives, and this was shown to outperform existing methods in several key respects. The stability and convergence of the new method were rigorously established.

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Yang, Qianqian. "Novel analytical and numerical methods for solving fractional dynamical systems." Thesis, Queensland University of Technology, 2010. https://eprints.qut.edu.au/35750/1/Qianqian_Yang_Thesis.pdf.

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During the past three decades, the subject of fractional calculus (that is, calculus of integrals and derivatives of arbitrary order) has gained considerable popularity and importance, mainly due to its demonstrated applications in numerous diverse and widespread fields in science and engineering. For example, fractional calculus has been successfully applied to problems in system biology, physics, chemistry and biochemistry, hydrology, medicine, and finance. In many cases these new fractional-order models are more adequate than the previously used integer-order models, because fractional deri

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Aldoghaither, Abeer. "Methods and Algorithms for Solving Inverse Problems for Fractional Advection-Dispersion Equations." Diss., 2015. http://hdl.handle.net/10754/582312.

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Fractional calculus has been introduced as an e cient tool for modeling physical phenomena, thanks to its memory and hereditary properties. For example, fractional models have been successfully used to describe anomalous di↵usion processes such as contaminant transport in soil, oil flow in porous media, and groundwater flow. These models capture important features of particle transport such as particles with velocity variations and long-rest periods. Mathematical modeling of physical phenomena requires the identification of pa- rameters and variables from available measurements. This is refer

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Book chapters on the topic "Fractional advection-dispersion equation"

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Kelly, James F., and Mark M. Meerschaert. "The fractional advection-dispersion equation for contaminant transport." In Applications in Physics, Part B, edited by Vasily E. Tarasov. De Gruyter, 2019. http://dx.doi.org/10.1515/9783110571721-006.

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Sene, Ndolane. "Double Integration for the Fractional Advection-Dispersion Equation with Nonsingular Derivative." In Applications of Fractional Calculus to Modeling in Dynamics and Chaos. Chapman and Hall/CRC, 2022. http://dx.doi.org/10.1201/9781003006244-13.

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Allwright, A., and A. Atangana. "Upwind-Based Numerical Approximation of a Space-Time Fractional Advection-Dispersion Equation for Groundwater Transport Within Fractured Systems." In Studies in Systems, Decision and Control. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-11662-0_18.

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Conference papers on the topic "Fractional advection-dispersion equation"

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Li, Changpin, and Zhengang Zhao. "On the finite element method for the time-space fractional advection dispersion equation." In 2010 IEEE/ASME International Conference on Mechatronic and Embedded Systems and Applications (MESA). IEEE, 2010. http://dx.doi.org/10.1109/mesa.2010.5551995.

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Aldoghaither, Abeer, Taous-Meriem Laleg-Kirati, and Da-Yan Liu. "The determination of an unknown source for a space fractional advection dispersion equation." In 2014 IEEE/ASME 10th International Conference on Mechatronic and Embedded Systems and Applications (MESA). IEEE, 2014. http://dx.doi.org/10.1109/mesa.2014.6935590.

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Fomin, Sergei, Vladimir Chugunov, and Toshiyuki Hashida. "Application of Fractional Derivatives for Simulating Diffusion Into Porous Matrix in Mathematical Modeling of the Contaminant Transport in a Confined Fractured Porous Aquifer." In ASME 2006 International Mechanical Engineering Congress and Exposition. ASMEDC, 2006. http://dx.doi.org/10.1115/imece2006-16138.

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Solute transport in the fractured porous confined aquifer is modeled by the advection-dispersion equation with fractional time derivative of order γ, which may vary from 0 to 1. Accounting for diffusion in the surrounding rock mass leads to the introduction of an additional fractional time derivative of order 1/2 in the equation for solute transport. The closed-form solutions for concentrations in the aquifer and surrounding rocks are obtained for the arbitrary time-dependent source of contamination located in the inlet of the aquifer. Based on these solutions, different regimes of contaminati

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Liu, Fawang, Pinghui Zhuang, and Kevin Burrage. "Stability and Convergence of Implicit Numerical Methods for a Class of Fractional Advection-Dispersion Models." In ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/detc2011-47071.

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In this paper, a class of fractional advection-dispersion models (FADM) is investigated. These models include five fractional advection-dispersion models: the immobile, mobile/immobile time FADM with a temporal fractional derivative 0 < γ < 1, the space FADM with skewness, both the time and space FADM and the time fractional advection-diffusion-wave model with damping with index 1 < γ < 2. They describe nonlocal dependence on either time or space, or both, to explain the development of anomalous dispersion. These equations can be used to simulate regional-scale anomalous dispersion

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Shan, Hua, and Sung-Eun Kim. "Numerical Study of Advection Schemes for Interface Capturing in a Volume of Fluid Method on Unstructured Meshes." In ASME-JSME-KSME 2011 Joint Fluids Engineering Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/ajk2011-04029.

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In solving naval hydrodynamics problems using computational fluid dynamics (CFD), the moving free surface between air and water introduces extra difficulties to numerical methods, since the material property jumps across the interface and the time-dependent free surface position becomes part of the solution. Engineering applications often require a flexible and robust solver for incompressible multi-phase viscous flows with the capability of capturing the interface. In the volume of fluid (VOF) method, the interface is captured by directly solving the convection transport equation of volume fr

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Sˇtrubelj, Luka, and Iztok Tiselj. "Numerical Simulation of Rayleigh-Taylor Instability With Two-Fluid Model and Interface Sharpening." In ASME 2008 Fluids Engineering Division Summer Meeting collocated with the Heat Transfer, Energy Sustainability, and 3rd Energy Nanotechnology Conferences. ASMEDC, 2008. http://dx.doi.org/10.1115/fedsm2008-55063.

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The free surface flows are successfully modeled with one of the existing free surface models, such as: level set method, volume of fluid method, front tracking method, two-fluid model (two momentum equations) with modified interphase force and some others. The main disadvantage of the two-fluid model used for simulations of free surface flows is numerical diffusion of the interface, which can be significantly reduced as presented in this paper. The interface is sharpened with the conservative level set method, where after the advection step of volume fraction the numerical diffusion of the int

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