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{  PERIODIC_CONTAMINANT.PDE

  This problem computes the flow of contaminant pulses in a periodic channel section.

}

 

title 'Periodic Contaminant transport in 2D channel'

 

variables

  c(0.01)

 

select

  ngrid=40

 

definitions

  Lx = 5       Ly = 1.5

  p0 = 2

  dens = 1

  visc0 = 0.04

  visc = visc0

  vxx = -(p0/(2*visc*(2*Lx)))*(Ly^2-y^2)       { open-channel x-velocity }

  u = 0.5*vxx  

  v = 0  

  speed = sqrt(u^2+v^2)

 

  Re = globalmax(speed)*(Ly/2)/(visc0/dens)

 

  Kc = 0.002       { contaminant diffusivity }

  wid=0.3

  c0=1

  cinput = c0*exp(-(x^2+(y-Ly/2)^2)/wid^2)

 

Initial Values

  c = cinput

 

equations

  c:  dt(c) + u*dx(c) + v*dy(c) = div(Kc*grad(c))

 

boundaries

  region 1

    start(-Lx,0)

    load(c)=0

      line to (Lx,0)

    periodic(x-2*Lx,y)

              line to (Lx,Ly)

 

    mesh_spacing=100

    load(c)=0

              line to(-Lx,Ly)

      line to close

 

 

time 0 to 10

 

monitors

  for cycle = 10

  contour(speed) report(Re)

  contour(c) range(0,1) report(Re)

 

plots

  for t=0 by 0.2 to endtime

  contour(c) range(0,1) painted report(Re)

  contour(u) report(Re)

  contour(v) report(Re)

  contour(speed) painted report(Re)

  vector(u,v) as "flow"   report(Re)

  contour(dx(u)+dy(v)) as "Continuity Error"

 

  history(integral(c)) range(0,1.2*integral(cinput))

  history(c) at (0,0.8) (2,0.8) (3,0.8) (4,0.8) (Lx,0)

 

end