ADE                  package:SoPhy                  R Documentation

_A_d_v_e_c_t_i_o_n-_d_i_s_p_e_r_s_i_o_n _e_q_u_a_t_i_o_n

_D_e_s_c_r_i_p_t_i_o_n:

     Solution of a simple advection-dispersion equation

_U_s_a_g_e:

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

_A_r_g_u_m_e_n_t_s:

       z: vector of distances from surface

    time: vector of time points

      C0: constant concentration at the surface

dispersion: constant dispersion coefficient

velocity: constant velocity

_D_e_t_a_i_l_s:

     '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'.

_V_a_l_u_e:

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

_A_u_t_h_o_r(_s):

     Martin Schlather, martin.schlather@cu.lu <URL:
     http://www.cu.lu/~schlathe>

_R_e_f_e_r_e_n_c_e_s:

        *  Schlather, M. and Huwe, B. (2003) The use of the language
           interface of R: two examples for modelling water flux and
           solute transport. _Computers & Geosciences_.

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

_E_x_a_m_p_l_e_s:

     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)

