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{  RICHARDS.PDE

 

 A solution of Richards' equation in 1D.

 Constant negative head at surface, unit gradient at bottom.

 This problem runs slowly, because the very steep wave front

 requires small cells and small timesteps to track accurately.

 

 submitted by Neil Soicher of University of Hawaii.

}

title "1-D Richard's equation"

coordinates

   cartesian1('y')

variables

   h (1)

definitions

   thr = 0.2

   ths = 0.58

   alpha = .08

   n = 1.412

   ks = 10

  {Using Van Genuchten parameters for water content (wc),

    water capacitance (C=d(wc)/dh), effecive saturation (se),

    and hydraulic Conductivity (k) }

   m  = 1-1/n

   wc = if h<0 then thr+(ths-thr)*(1+(abs(alpha*h))^n)^(-m) else ths

   C  = ((1-n)*abs(-alpha*h)^n*(1+abs(-alpha*h)^n)^((1/n)-2)*(ths-thr))/h

   se = (wc-thr)/(ths-thr)

   k  = ks*sqrt(se)*(1-(1-se^(1/m))^m)^2

initial values

   h = 199*exp(-(y-100)^2)-200

equations

   h : dy(k*(dy(h)+1)) = C*dt(h)

boundaries

  region 1

      start(0)

      line to (100) point value(h) = -1

front(h+150,1)

time 0 to 2

monitors

  for cycle=10

      elevation(c) from (100) to (0) as "capacitance"

      elevation(h) from (100) to (0) as "pressure"

      elevation(k) from (100) to (0) log as "conductivity"

      grid(y) from (100) to (0)

plots

    for t=0.001 0.01 0.1 1

      elevation(h) from (100) to (0) as "pressure"

      elevation(c) from (100) to (0) as "capacitance"

      elevation(k) from (100) to (0) log as "conductivity"

      grid(y) from (100) to (0)

end

 


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