Numerical Solution of Fractional Advection-Dispersion Equation

By Z. Deng, Vijay P. Singh, L. Bengtsson. 2004

155 citations recorded by the source corpus.

Subfields: Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/2928dffb9545e52d146b3138a93b71ce6db17dbc

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Citations in the corpus

Finite di$erence approximations for fractional advection-dispersion &ow equations (2004, methodology): “Keywords: Finite di$erence approximation; Stability; Backward Euler method; Implicit Euler method; Radial dispersion; Radial advection; Fractional di$usion; Fractional derivative; Fractional advection–dispersion; Numerical fractional ADE”
Time and space nonlocalities underlying fractional-derivative models: Distinction and literature review of field applications (2009, methodology): “This similarity might be the motivation behind the application of the space nonlocal model to simulate the retention process (see for example, [12,45,46,74,143]).”
Tempered anomalous diffusion in heterogeneous systems (2008, background): “[15] Dye tracer concentration measured along different reaches of the Missouri River between Sioux City, Iowa, and Plattsmouth, Nebraska (regional-scale, 200-km-long) exhibits a slow decay rate at late time (see symbols in Figure 2b) that is overestimated by the single-rate mass transfer model [Deng”
A second-order accurate numerical approximation for the fractional diffusion equation (2006, methodology): “Several different first-order accurate numerical methods to solve fractional diffusion equations have been presented before [3,4,6,7,9,10].”
Gegenbauer spectral method for time‐fractional convection–diffusion equations with variable coefficients (2015, methodology): “In [10], a fractional advection–dispersion equation is derived by extending Fick’s first law from isotropic media to heterogeneous media and is particularly suitable for description of the highly skewed and heavy-tailed dispersion processes observed in rivers and other natural media.”
A finite element solution for the fractional advection–dispersion equation (2008, methodology): “Besides, some numerical solutions of the FADE only take the left-handed fractional derivative into account [11,23,25,49,50], implying that the backward transition of solute particles that is slower than the average velocity is eliminated.”
Parameter estimation for fractional transport: A particle‐tracking approach (2009, unknown): “Parameter estimation for fractional transport:”
Finite difference methods for two-dimensional fractional dispersion equation (2006, methodology): “A numerical example is included, along with its exact analytical solution, to validate the method and its order of convergence.”
A Petrov–Galerkin finite element method for variable-coefficient fractional diffusion equations (2015, background): “It was also reported that retention of contaminant particles in river beds and eddy pools causes a power-law trailing edge in the concentration profile, which corresponds to (1) with θ = 0 [26,27].”
FracFit: A robust parameter estimation tool for fractional calculus models (2017, methodology): “FRACFIT PARAMETER ESTIMATION 2563 with b521, which agrees with earlier studies [Chakraborty et al., 2009; Deng et al., 2004].”