A distributed-order time fractional derivative model for simulating bimodal sub-diffusion in heterogeneous media

[1]  Groundwater contamination. , 1984, Science.

[2]  M. V. Genuchten,et al.  Flux-Averaged and Volume-Averaged Concentrations in Continuum Approaches to Solute Transport , 1984 .

[3]  Mark N. Goltz,et al.  Using the method of moments to analyze three-dimensional diffusion-limited solute transport from tem , 1987 .

[4]  E. Simpson,et al.  Laboratory evidence of the scale effect in dispersion of solutes in porous media , 1987 .

[5]  K. Novakowski An evaluation of boundary conditions for one-dimensional solute transport: 2. Column experiments , 1992 .

[6]  A. Valocchi,et al.  Stochastic analysis of the transport of kinetically sorbing solutes in aquifers with randomly heterogeneous hydraulic conductivity , 1993 .

[7]  R. Hills,et al.  Solute transport through large uniform and layered soil columns , 1993 .

[8]  M. V. Genuchten,et al.  A dual-porosity model for simulating the preferential movement of water and solutes in structured porous media , 1993 .

[9]  S. Gorelick,et al.  Multiple‐Rate Mass Transfer for Modeling Diffusion and Surface Reactions in Media with Pore‐Scale Heterogeneity , 1995 .

[10]  Sheldon M. Ross Introduction to Probability Models. , 1995 .

[11]  K. Huang,et al.  Experimental investigation of solute transport in large, homogeneous and heterogeneous, saturated soil columns , 1995 .

[12]  Graham E. Fogg,et al.  Random-Walk Simulation of Transport in Heterogeneous Porous Media: Local Mass-Conservation Problem and Implementation Methods , 1996 .

[13]  Liwang Ma,et al.  Solute Transport in Soils Under Conditions of Variable Flow Velocities , 1996 .

[14]  Naomichi Hatano,et al.  Dispersive transport of ions in column experiments: An explanation of long‐tailed profiles , 1998 .

[15]  J. Klafter,et al.  The random walk's guide to anomalous diffusion: a fractional dynamics approach , 2000 .

[16]  J. Feyen,et al.  Comparison of flux and resident concentrations in macroporous field soils. , 2000 .

[17]  D. Benson,et al.  The fractional‐order governing equation of Lévy Motion , 2000 .

[18]  Sean Andrew McKenna,et al.  On the late‐time behavior of tracer test breakthrough curves , 2000 .

[19]  D. Benson,et al.  Application of a fractional advection‐dispersion equation , 2000 .

[20]  Peter K. Kitanidis,et al.  Macroscopic behavior and random‐walk particle tracking of kinetically sorbing solutes , 2000 .

[21]  B Berkowitz,et al.  Application of Continuous Time Random Walk Theory to Tracer Test Measurements in Fractured and Heterogeneous Porous Media , 2001, Ground water.

[22]  I. M. Sokolov,et al.  Fractional Fokker-Planck equation for ultraslow kinetics , 2003 .

[23]  Chunmiao Zheng,et al.  Analysis of Solute Transport in Flow Fields Influenced by Preferential Flowpaths at the Decimeter Scale , 2003, Ground water.

[24]  Rina Schumer,et al.  Fractal mobile/immobile solute transport , 2003 .

[25]  Christoph Hinz,et al.  Non‐Fickian transport in homogeneous unsaturated repacked sand , 2004 .

[26]  Francesco Mainardi,et al.  Simply and multiply scaled diffusion limits for continuous time random walks , 2005 .

[27]  Brian Berkowitz,et al.  Non‐Fickian transport and multiple‐rate mass transfer in porous media , 2008 .

[28]  M. Meerschaert,et al.  Stochastic model for ultraslow diffusion , 2006 .

[29]  D. Benson,et al.  Relationship between flux and resident concentrations for anomalous dispersion , 2006 .

[30]  Peter Salamon,et al.  Modeling mass transfer processes using random walk particle tracking , 2006 .

[31]  M. Dentz,et al.  Modeling non‐Fickian transport in geological formations as a continuous time random walk , 2006 .

[32]  Boris Baeumer,et al.  Predicting the Tails of Breakthrough Curves in Regional‐Scale Alluvial Systems , 2007, Ground water.

[33]  Brian D. Wood,et al.  Mass transfer process in a two‐region medium , 2008 .

[34]  John M. Zachara,et al.  Scale‐dependent desorption of uranium from contaminated subsurface sediments , 2008 .

[35]  M. Meerschaert,et al.  Tempered anomalous diffusion in heterogeneous systems , 2008 .

[36]  D. Benson,et al.  Moment analysis for spatiotemporal fractional dispersion , 2008 .

[37]  Boris Baeumer,et al.  Particle tracking for time-fractional diffusion. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[38]  D. Benson,et al.  Time and space nonlocalities underlying fractional-derivative models: Distinction and literature review of field applications , 2009 .

[39]  Gerardo Severino,et al.  Darcian preferential water flow and solute transport through bimodal porous systems: experiments and modelling. , 2009, Journal of contaminant hydrology.

[40]  Chaopeng Shen,et al.  An efficient space-fractional dispersion approximation for stream solute transport modeling , 2009 .

[41]  Yury Luchko,et al.  BOUNDARY VALUE PROBLEMS FOR THE GENERALIZED TIME-FRACTIONAL DIFFUSION EQUATION OF DISTRIBUTED ORDER , 2009 .

[42]  S. Feng,et al.  Comparison of alternative models for simulating anomalous solute transport in a large heterogeneous soil column , 2009 .

[43]  Kai Diethelm,et al.  Numerical analysis for distributed-order differential equations , 2009 .

[44]  Mark M. Meerschaert,et al.  Tempered stable Lévy motion and transient super-diffusion , 2010, J. Comput. Appl. Math..

[45]  Henning Prommer,et al.  A field‐scale reactive transport model for U(VI) migration influenced by coupled multirate mass transfer and surface complexation reactions , 2010 .

[46]  M. Dentz,et al.  Distribution- versus correlation-induced anomalous transport in quenched random velocity fields. , 2010, Physical review letters.

[47]  Marco Bianchi,et al.  Lessons Learned from 25 Years of Research at the MADE Site , 2011, Ground water.

[48]  David A. Benson,et al.  Comparison of Fickian and temporally nonlocal transport theories over many scales in an exhaustively sampled sandstone slab , 2011 .

[49]  H. Scher,et al.  Non-Fickian transport in porous media with bimodal structural heterogeneity. , 2011, Journal of contaminant hydrology.

[50]  F. Leij,et al.  Solute transport in dual‐permeability porous media , 2012 .

[51]  Ninghu Su,et al.  Distributed-order infiltration, absorption and water exchange in mobile and immobile zones of swelling soils , 2012 .

[52]  Enrico Zio,et al.  A novel particle tracking scheme for modeling contaminant transport in a dual‐continua fractured medium , 2012 .

[53]  X. Sanchez‐Vila,et al.  On the formation of multiple local peaks in breakthrough curves , 2015 .

[54]  Mark M. Meerschaert,et al.  Modeling mixed retention and early arrivals in multidimensional heterogeneous media using an explicit Lagrangian scheme , 2015 .

[55]  F. Leij,et al.  Modeling Transport in Dual-Permeability Media with Unequal Dispersivity and Velocity , 2015 .

[56]  S. Pozdniakov,et al.  Simulation of Hydraulic Heterogeneity and Upscaling Permeability and Dispersivity in Sandy-Clay Formations , 2015, Mathematical Geosciences.

[57]  Hongguang Sun,et al.  Bounded fractional diffusion in geological media: Definition and Lagrangian approximation , 2016 .

[58]  Tracer travel and residence time distributions in highly heterogeneous aquifers: Coupled effect of flow variability and mass transfer , 2016 .

[59]  H. Yeh,et al.  Investigation of flow and solute transport at the field scale through heterogeneous deformable porous media , 2016 .

[60]  Hongguang Sun,et al.  Can a Time Fractional‐Derivative Model Capture Scale‐Dependent Dispersion in Saturated Soils? , 2017, Ground water.

[61]  V. Hallet,et al.  Double-peaked breakthrough curves as a consequence of solute transport through underground lakes: a case study of the Furfooz karst system, Belgium , 2018, Hydrogeology Journal.

[62]  G. Moradi,et al.  Modelling solute transport in homogeneous and heterogeneous porous media using spatial fractional advection-dispersion equation , 2017 .

[63]  N. Su The fractional Boussinesq equation of groundwater flow and its applications , 2017 .

[64]  Hongbin Zhan,et al.  An Experimental Study on Solute Transport in One-Dimensional Clay Soil Columns , 2017 .

[65]  B. Mehdinejadiani Estimating the solute transport parameters of the spatial fractional advection-dispersion equation using Bees Algorithm. , 2017, Journal of contaminant hydrology.

[66]  C. Zheng,et al.  Comparison of Time Nonlocal Transport Models for Characterizing Non-Fickian Transport: From Mathematical Interpretation to Laboratory Application , 2018, Water.

[67]  Trifce Sandev,et al.  Distributed-order wave equations with composite time fractional derivative , 2018, Int. J. Comput. Math..

[68]  O. Cirpka,et al.  A mobile-mobile transport model for simulating reactive transport in connected heterogeneous fields , 2018 .

[69]  X. Mou,et al.  Experimental comparison of thermal and solute dispersion under one‐dimensional water flow in saturated soils , 2019, European Journal of Soil Science.

[70]  HongGuang Sun,et al.  Distributed order Hausdorff derivative diffusion model to characterize non-Fickian diffusion in porous media , 2019, Commun. Nonlinear Sci. Numer. Simul..

[71]  Z. Wen,et al.  A new model approach for reactive solute transport in dual-permeability media with depth-dependent reaction coefficients , 2019, Journal of Hydrology.

[72]  Hongguang Sun,et al.  A review on variable-order fractional differential equations: mathematical foundations, physical models, numerical methods and applications , 2019, Fractional Calculus and Applied Analysis.

[73]  C. Zheng,et al.  Super-diffusion affected by hydrofacies mean length and source geometry in alluvial settings , 2020, Journal of Hydrology.

[74]  G. Moradi,et al.  An experimental study on scale dependency of fractional dispersion coefficient , 2020, Arabian Journal of Geosciences.

[75]  Bill X. Hu,et al.  An efficient approximation of non-Fickian transport using a time-fractional transient storage model , 2020 .

[76]  B. Mehdinejadiani,et al.  Study on non-Fickian behavior for solute transport through porous media , 2020, ISH Journal of Hydraulic Engineering.