Re: Calculation of velocity with continuity equation

[Jonathan Guyer]

On Jan 8, 2009, at 10:27 AM, Etienne Rivard wrote:


Hello Jonathan,

Once again, thank you for your answer.

I'm glad to help... if you can call it that


How does $v^*$ appear in your other equations? Is it possible that  
one
of them is more naturally solved for velocity?

I definitely don't think so. The other equations, in cartesian  
coordinates
and without coordinate change have the following form


\[
\frac{\partial}{\partial t} (cx)
+ \nabla \cdot (cv^*x)
= \nabla \cdot (c D \nabla x)
\]

and they are necessary to calculate $x$, the mole fraction.


The legend has it that the velocity must be calculated from continuity

I want to reiterate that fluids aren't my thing, but perhaps my  
naiveté can be of some benefit.

Do you not have a momentum equation? In Daniel's work, I believe he  
solves the momentum equation for velocity. Something like
\[
\frac{\partial}{\partial t} (cv^*)
+ \nabla\cdot (c v^* v^*)
+ dissipation terms
= 0
\]


But last night, I reread a thesis I have and I realized that the
convection can be neglected. Which of course solves the problem with
velocity. I will go with this approach now because I need results  
for a
conference in early spring and I'm confident it will give satisfactory
results.

That sounds like it may be the most expedient solution. Good luck.