I want to solve the time-dependent convection-diffusion equation and am testing
my code on a simple 1D case.
The flow field is a simple constant velocity. I've set D = 0, so no diffusion
should happen at all.
This system represents a little plug of high-concentration solute in a solvent
that should flow down the tube
without spreading. Problem is that I get lots of spreading even when I set cell
size and time-step very small.
Can anyone see what I'm doing wrong?
# Tube dimensions (cm)
xlen = 1.0
flow_vel = 0.1
D = 0.0
# number of cells
nx = 1000
dx = xlen/nx
Lx = dx*nx
mesh = Grid1D(dx=dx,nx=nx)
phi = CellVariable(name = "solution variable",
mesh = mesh,
value = 0.)
x = mesh.cellCenters[0]
phi.setValue(1.0, where=(x > 2*Lx/3. - Lx/20.0) & (x < 2*Lx/3.0 + Lx/20.0))
ConvCoef = [flow_vel]
eq = TransientTerm() ==
(DiffusionTerm(coeff=D)+PowerLawConvectionTerm(coeff=ConvCoef))
if __name__ == '__main__':
viewer = Viewer(vars=phi, datamin=0., datamax=1.)
viewer.plot()
timeStepDuration = 0.01
steps = 800
for step in range(steps):
eq.solve(var=phi,dt=timeStepDuration)
if __name__ == '__main__':
viewer.plot()
Thanks!
Richard
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