ADE {SoPhy}R Documentation

Advection-dispersion equation

Description

Solution of a simple advection-dispersion equation

Usage

  ADE(z, time, C0, dispersion, velocity) 

Arguments

z vector of distances from surface
time vector of time points
C0 constant concentration at the surface
dispersion constant dispersion coefficient
velocity constant velocity

Details

ADE solves the PDE

d C(z,t) / d t = D * d^2 C(z,t) / d z^2 - v * d C(z,t) / d z

on the one-dimensional semi-finite column, i.e. z in [0,infty]. Here D is the dispersion coefficient and v the velocity. Further, C(infty,t)=0 for all t and C(z,0)=0 for all z. Further, C(0,t)=C0.

Value

ADE calculates the concentration on a grid given by z and time, i.e., ADE returns a (length(z) x length(time))-matrix.

Author(s)

Martin Schlather, martin.schlather@math.uni-goettingen.de http://www.stochastik.math.uni-goettingen.de/institute

References

Schlather, M. and Huwe, B. (2004) The use of the language interface of R: two examples for modelling water flux and solute transport. Computers & Geosciences 30, 197-201.

Tindall, J.A. and Kunkel, J.R (1999) Unsaturated Zone Hydrology for Scientists and Engineers. New Jersey: Prentice-Hall.

Examples

par(cex=1.5, mar=c(4.2,4,0.2,0.4))
z <- ADE(z=1:100, t=10^(0:3), C0=1, d=1, v=1)
matplot(z, outer(-1:-100, rep(1,4)), type='l',
        xlab='concentration', ylab='z', 
        lwd=3, cex.lab=1.5, cex.axis=1.5, col=1)
legend(1.0, -100, legend=paste('t=', 10^(0:3), sep=''), xj=1, yj=0,
        lwd=3, lty=1:4, cex=1.5, col = 1)

[Package SoPhy version 1.0.34 Index]