{ WATER.PDE }
{
This problem shows the flow of water to two wells, through soil regions of
differing porosity. It also displays the ability of FlexPDE to grid features
of widely varying size.
}
title 'Groundwater flow to two wells'
definitions
k { no value is required, as long as it appears later }
s = 0 { no volumetric source }
k1 = 0.1 { high porosity value }
k2 = 1.0e-7 { low porosity value }
sx1 = 0.7 sy1 = 0.4 { well 1 location }
sx2 = 0.5 sy2 = 0.2 { well 2 location }
srad = 0.001 { well radius = one thousandth of domain size }
w = 0.05 { a zoom window size }
px = 0.4 py = 0.4 { percolation pond center }
pr = 0.025 { percolation pond radius }
ps = 1e-4 { percolation rate }
Variables
h
equations
div(k*grad(h)) + s = 0
boundaries
Region 1 { The domain boundary, held at constant pressure head }
k=k1
start(0,0)
value(h)=0 line to (0.25,-0.1)
to (0.45,-0.1)
to (0.65,0)
to (0.95,0.1)
to (0.95,0.4)
to (0.75,0.6)
to (0.45,0.65)
to (0,0.4)
to close
{ Two wells, held at constant draw-down depths }
start(sx1,sy1-srad)
value(h) = -1 arc(center=sx1,sy1) angle=-360
start(sx2,sy2-srad)
value(h) = -2 arc(center=sx2,sy2) angle=-360
Region 2 { Some regions of low porosity }
k=k2
start(0,0) line to (0.25,-0.1)
to (0.45,-0.1)
to (0.45,0.05)
to (0,0.05)
to close
start(0.95,0.1) line to (0.95,0.3)
to (0.65,0.3)
to (0.65,0)
to close
start(0.3,0.3) line to (0.5,0.4)
to (0.5,0.6)
to (0.3,0.5)
to close
Region 3 { A percolation pond }
k = k2
s = ps { percolation rate }
start (px,py-pr) arc(center=px,py) angle=360
monitors
contour(h)
plots
grid(x,y)
grid(x,y) zoom(sx1-w/2,sy1-w/2,w,w)
grid(x,y) zoom(sx2-w/2,sy2-w/2,w,w)
contour(h) as 'Head'
contour(h) as 'Head' zoom(0.65,0.35,0.1,0.1)
surface(h) as 'Head'
end