Possible problems of scale dependency in applications of the three‐dimensional fractional advection‐dispersion equation to natural porous media

By Silong Lu, Fred J. Molz III, George J. Fix III. 2002

60 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Computational Mechanics, Environmental Engineering

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Civil and Structural Engineering

1. John Paul Roop
2. Hongguang Sun
3. J. Roof
4. Lu Lu
5. G. Em Karniadakis
6. Yong Zhang
7. Wen Chen
8. George J. Fix III

In Computational Mechanics

1. Lu Lu
2. John Paul Roop
3. Guofei Pang
4. J. Roof
5. Wen Chen
6. G. Em Karniadakis
7. Yong Zhang
8. George J. Fix III

In Environmental Engineering

1. John Paul Roop
2. Hongguang Sun
3. J. Roof
4. G. Em Karniadakis
5. Lu Lu
6. Yong Zhang
7. Donald M. Reeves
8. Wen Chen

Citations in the corpus

• fPINNs: Fractional Physics-Informed Neural Networks (2018, background): “ethefirstattempttosolvetheforwardandtheinverseproblemsforspacetime-fractional ADEs defined in complex-geometry domains. For forward problems, there have beensomeworksonsolving3Dspace-fractionalADEs. In [36,37,38,39],onlythe3Dextension oftheRieszspace-fractionalderivativesisconsidered,whichdiffersfromth”
• Computational aspects of FEM approximation of fractional advection dispersion equations on bounded domains in R 2 (2006, methodology): “For our calculations, we use the graphical representation of the data at days 27, 132, 224, and 328 in [ 12 ] .I n[2], the MADE tracer data was spatially averaged into a 1-D model which was found to follow dispersion corresponding to a 1-D FADE with = 0.55 (order of differential operator = 1.1), a =”
• Least squares finite-element solution of a fractional order two-point boundary value problem (2004, methodology): “To date, all the analysis of fractional differential equations has been for the infinite domain, using the Fourier transform [1, 6 ].”
• Variational solution of fractional advection dispersion equations on bounded domains in ℝd (2007, unknown): “Next we define the fractional dimension Sobolev spaces and relate J L,θ(Ω) ( J α L,θ+π(Ω), J α S,θ(Ω) ) to H 0 (Ω) [8].”
• Use of a variable-index fractional-derivative model to capture transient dispersion in heterogeneous media. (2014, background): “This hypothesis keeps consistent with the space-dependent super-diffusive rate (Lu et al., 2002) and the possible spatial change of deposit properties at the MADE test site (Boggs et al., 1992) (see also Section 3.2).”