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Using dirac delta function as an initial condition
Posted 20 set 2010, 13:48 GMT-4 0 Replies
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I am trying to model the effect of gravity on brownian motion for which the general equation from Smoluchowski is
dw/dt = div . (qB^-2grad.w - KB^-1w).
Considering only the z direction then the simplified form is
dw/dt = D(d2w/dz2) + C(dw/dz) where D = kT/mB and C = (1-(p1/p2))g/B ( terms constituting D and C are known)
the boundary conditions would be
w-> dirac delta(z - z0) where z0 is the height of fluid measured from the bottom where z = 0.
D(dw/dz) + Cw = 0 at z = 0 for all time ( prevention of particles crossing z = 0 )
Currently i have tried using pde convection-diffusion equation (cdeq) (version 3.5a) and the initial value seems reasonable but questionable due to the negative u. Also, the solution does not progress much from the initial value solution as the expected result would be a curve shifting in time from from one extreme to the other in the shape of / similar to a gaussian distribution.
I'm not sure how to implement the dirac function as a initial concentration and i've tried using flc1hs(z-z0,1e-5) as the initial condition for the subdomain setting.
Any help would be welcome and thanks in advance.
Regards,
Chun Wei
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Hello Tan Chun Wei
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