Numerical Solution of the Problem of Anomalous Solute Transport in a Two-Dimensional Nonhomogeneous Porous Medium

FIGURE 2. Surfaces of for exponential forms of functions and at s, , , , , , , (а); (b); (c).


b)



y, m

x, m

x, m

y, m



а)



x, m

c)

y, m



FIGURE 3. Surfaces of for exponential forms of functions and at s, , , , , , , (а); (b); (c).


b)



а)

y, m

x, m

x, m

y, m





c)

x, m

y, m



FIGURE 4. Surfaces of for exponential functions and at s, , , , , , , (а); , (b); , (c).

Likewise, instead of functions and sinusoidal functions and were used and numerical results were obtained.

b)



а)

y, m

x, m

c)

x, m

y, m





x, m

y, m



FIGURE 5. Surfaces of for sinusoidal functions and at s, , , , , , , (а); (b); (c).


b)

а)

y, m

x, m

x, m

y, m







x, m

c)

y, m



FIGURE 6. Surfaces of for sinusoidal functions and at s, , , , , , , (а); (b); (c).

Figure 2, 3 illustrate the effect of the non-stationary parameter on concentration profiles. The directions of the concentration profiles of the solute transport in a certain position are higher for a smaller non-stationary parameter and lower for a larger one in both types of velocity, but the concentration profiles for a sinusoidal velocity decrease somewhat faster compared to the exponential velocity in both the and directions.

5. CONCLUSIONS

The problem of the solute transport in a two-dimensional porous medium with a fractal structure is formulated and numerically solved. It is shown that a decrease in the values of the order of the derivatives and in the convective-diffusion terms from 1 leads to "fast diffusion", the concentration profiles spread over the region more intensively, and the fields are smeared along the coordinate directions. Thus, the anomalous solute transport in the form of a fractional derivative along the coordinate directions leads to "fast diffusion".