ADE {SoPhy} | R Documentation |
Solution of a simple advection-dispersion equation
ADE(z, time, C0, dispersion, velocity)
z |
vector of distances from surface |
time |
vector of time points |
C0 |
constant concentration at the surface |
dispersion |
constant dispersion coefficient |
velocity |
constant velocity |
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
.
ADE
calculates the concentration on a grid given by
z
and time
, i.e.,
ADE
returns a (length(z)
x length(time)
)-matrix.
Martin Schlather, martin.schlather@math.uni-goettingen.de http://www.stochastik.math.uni-goettingen.de/institute
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.
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)