Abstract
Standard finite difference and finite element solution methods of the pollutant transport equation require restrictive spatial discretization in order to avoid numerical dispersion. The random walk method offers a robust alternative if for reasons of calculational effort discretization requirements cannot be met. The method is discussed for the case of an ideal tracer starting out from the Ito-Fokker-Planck-equation. Features such as chemical reactions and adsorption can be incorporated. Besides being an alternative to other solution methods for the classical transport equation the random walk deserves attention due to its generalizability allowing the incorporation of non-Fickian dispersion. A shortcoming of the method results from the general roughness of simulated distributions in space and time due to statistical fluctuations and resolution problems. The method is applied to a field case of groundwater pollution by chlorohydrocarbons.
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Abbreviations
- c:
-
concentration (g m-3) (index m: mobile phase, index im: immobile phase)
- D :
-
dispersion tensor with components Dxx, Dxy, Dyx, Dyy (m2 s-1)
- D:
-
fractal dimension
- M:
-
pollutant mass (index P: particle) (kg)
- n:
-
porosity (index e: effective, index m: mobile, index im: immobile)
- P:
-
time constant for reaching asymptotic dispersion (d)
- R:
-
retardation factor
- t:
-
time (days)
- Δt:
-
time step (days)
- ū:
-
vector of pore velocity with components ux, uy (m day-1)
- u:
-
modulus of ū (m day-1)
- x, y:
-
horizontal coordinates (m)
- Δx, Δy:
-
grid-distances in x- and y- direction (m)
- X:
-
uniformly distributed random variable from the interval [0,1]
- Z(t, H):
-
fractional Gaussian noise
- Z, Z1, Z2 :
-
normally distributed random variable with average 0 and standard deviation 1
- α:
-
exchange coefficient (day-1)
- αL :
-
longitudinal dispersivity (m)
- αT :
-
transverse dispersivity (m)
- ∇⃑:
-
nabla operator (∂/∂x, ∂/∂y)
- λ:
-
chemical reaction rate constant (day-1)
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Kinzelbach, W. (1988). The Random Walk Method in Pollutant Transport Simulation. In: Custodio, E., Gurgui, A., Ferreira, J.P.L. (eds) Groundwater Flow and Quality Modelling. NATO ASI Series, vol 224. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-2889-3_15
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DOI: https://doi.org/10.1007/978-94-009-2889-3_15
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