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# contaminant_transport

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# contaminant_transport   { CONTAMINANT_TRANSPORT.PDE

This example shows the use of sequenced equations in the calculation of steady-state

contaminant transport  in which the fluid properties are independent of the contaminant

concentration.

Fluid equations are solved first on each grid refinement, then the contaminant

concentration is updated.

The problem is a modification of the example CHANNEL.PDE.

}

title 'Contaminant transport in 2D channel'

select

errlim = 0.005

ngrid = 40

variables

u(0.1)

v(0.01)

p(1)

c(0.01)

definitions

Lx = 5       Ly = 1.5

p0 = 2

speed2 = u^2+v^2

speed = sqrt(speed2)

dens = 1

visc = 0.04

vxx = -(p0/(2*visc*(2*Lx)))*y^2   { open-channel x-velocity with drag at the bottom }

rball=0.4

cut = 0.1   { value for bevel at the corners of the obstruction }

penalty = 100*visc/rball^2

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

Kc = 0.01   { contaminant diffusivity }

initial values

u =  vxx   v=0  p = p0*x/Lx

equations

u:  visc*div(grad(u)) - dx(p) = dens*(u*dx(u) + v*dy(u))

v:  visc*div(grad(v)) - dy(p) = dens*(u*dx(v) + v*dy(v))

then

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

boundaries

region 1

start(-Lx,0)

value(u) = 0   value(v) = 0   load(p) = 0 natural(c)=0

line to (Lx/2-rball,0)

to (Lx/2-rball,rball) bevel(cut)

to (Lx/2+rball,rball) bevel(cut)

to (Lx/2+rball,0)

to (Lx,0)

mesh_spacing=Ly/20

load(u) = 0 value(v) = 0 value(p) = p0 value(c) = Upulse(y,y-Ly/3)

line to (Lx,Ly)

mesh_spacing = 100

line to (-Lx,Ly)

value(p) = 0

line to close

monitors

contour(speed)

contour(c)

plots

contour(c) report(Re)

contour(u) report(Re)

contour(v) report(Re)

contour(speed) painted report(Re)

vector(u,v) as "flow"   report(Re)

contour(p) as "Pressure" painted

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

elevation(u) from (-Lx,0) to (-Lx,Ly)

elevation(u) from (0,0)   to (0,Ly)

elevation(u) from (Lx/2,0)to (Lx/2,Ly)

elevation(u) from (Lx,0) to (Lx,Ly)

end