Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » sci.math.* » sci.math.num-analysis.independent

Topic: 1D Convection-diffusion equation with problematic boundary condition
Replies: 0  

Advanced Search

Back to Topic List Back to Topic List  
ikkim

Posts: 1
Registered: 2/4/13
1D Convection-diffusion equation with problematic boundary condition
Posted: Feb 4, 2013 5:20 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

Hi,

I'm analyzing a 1D problem in cylindrical geometry where the quantity of interest U(r,t) satisfies the convection-diffusion equation:

d/dt U(r,t) = divergence( F(r,t) ) + S(r,t)
where
F(r,t) = c(r)*grad U(r,t) - d(r)*U(r,t) is the radial flux of U(r,t)
and S(r,t) is the source

all with a nice and smooth initial condition U0(r) and known c(r), d(r) and S(r,t)

On axis (r=0) the natural boundary condition is given by F=0 (i.e. Flux=0)

I can solve the equation numerically if I use either a prescribed value for U(r=1,t)=UBnd(t) or if I give the flux through the outer boundary F(r=1,t)=FluxBnd(t).

The problem is that at the moment I only know that in steady state the flux through the outer boundary must match the steady state integrated source (otherwise it would not be a steady state situation).

In principle I only need to solve the equation near the steady state as the source is of the form S(r,t)=SS(r)+epsilon*SN(r,t) i.e. it is perturbed to produce perturbed U. However, even is this case I do not know what should I use for FluxBnd(t). Physically the perturbation in S(r,t) would show up delayed in FluxBnd(t) but I have no idea what is this delay. I still only know that <FluxBnd(t)> should match the average of the volume integrated source.

Can anybody tell me useful references for solving this type of problems or first of all point me in the right direction in defining a problem that can be solved. Would Fourier treatment for time help me or not with the boundary issue?

Thanks very much,
john



Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.