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, schlath@hsu-hh.de http://www.unibw-hamburg.de/WWEB/math/schlath/schlather.html

### 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 1.0.28 Index]