Should I Scale My Boundary Condition Values for Problem Where I Scaled Interior?

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bzz77
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Hello all:

I would very much appreciate advice on setting up a problem. Apologies in advance... This is probably a silly question--I'm more of a chemist than an engineer/math person!

I have written a code for calculating changes in concentration/mass within a domain over time, as new stuff flows in from a boundary. For discussion here, let's say the domain is rectangular and the new stuff is flowing in from the left (but the code should be able to handle any type of geometry).

In the code, I have scaled my concentrations/masses in the interior... So for any calculation, the resulting concentrations/masses will be for 1 m^3. This is all fine.

My question is, how do I deal with my boundary conditions as far as scaling? If I need to scale them, what would I scale them to? I can't use volume, because the boundary is a line.

To clarify, I have moles of chemical elements coming in at the boundaries. I start with moles of elements or mass of elements (density) in the interior, then I rescale the interior to 1 m^3. This scaling turns the moles or mass in the interior into molarity or molality.
 
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Your boundary conditions should have the same units as the body that you are integrating over. Normally you'd perform the same scaling operation on the boundary conditions that you did on the body. As you have observed, this will change the geometry of the problem - but only on paper.
 


Hi Simon. Thanks a lot! I'll go ahead and scale my boundary conditions to 1m^3 too.