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# richards

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# richards

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

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

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

grid(y)

plots

for t=0.001 by 0.001 to 0.01 0.1 by 0.1 to endtime

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

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

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

grid(y)

history(K) at (90) (95) (99) (100)

history(C) at (90) (95) (99) (100)

end "IE3vuxq/blOMIRLitV++FYgmXZuPz8D1+wvzXgpATJSsnTmsgWgSZOaLi+YOaMBsdxHjOXQUBxLPMVWceTZ+tzU0r6xbZ0Y9YaEBD8IG48nPCNezshKtEYPOYKh4ucdlKJWvPO8XzbScXAA9wKDowS86YuXXbtMkiY/S4U2KCpa"