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

In summary, the individual is seeking advice on setting up a problem involving changes in concentration and mass over time within a rectangular domain. The code they have written can handle any type of geometry and they have scaled their concentrations and masses to 1 m^3. However, they are unsure how to scale their boundary conditions, which are currently in moles or mass, as the boundary is a line. The solution is to perform the same scaling operation on the boundary conditions as was done on the body, which will result in a change in geometry on paper.
  • #1
bzz77
34
0
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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  • #2


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.
 
  • #3


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

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

1. Should I scale my boundary condition values if I scaled the interior of the problem?

It depends on the specific problem and the scaling method used. In some cases, scaling the boundary condition values may be necessary in order to maintain consistency with the scaled interior. However, in other cases, scaling the boundary conditions may not be necessary or may even result in incorrect solutions. It is important to carefully consider the effects of scaling on both the interior and boundary conditions before making a decision.

2. What are the potential consequences of not scaling my boundary condition values?

If the interior of the problem has been scaled, not scaling the boundary conditions could result in inconsistent or incorrect solutions. This is because the boundary conditions play a crucial role in determining the behavior of the system. If they are not scaled appropriately, it could lead to numerical instabilities or non-physical results.

3. How do I determine whether or not to scale my boundary conditions?

The decision to scale boundary conditions should be based on the specific problem at hand and the scaling method used for the interior. It is important to carefully analyze the effects of scaling on the boundary conditions and determine if it is necessary for maintaining consistency and accuracy in the solutions. Consulting with other experts in the field or conducting sensitivity analyses can also help in making this decision.

4. Are there any guidelines for scaling boundary condition values?

There is no one-size-fits-all guideline for scaling boundary conditions. The appropriate scaling method and values will depend on the specific problem and the desired outcome. Some common techniques include matching the scaling factor used in the interior, scaling based on the physical properties of the system, or using a non-dimensionalization approach. It is important to carefully consider the implications of each method and determine the most appropriate approach for the problem at hand.

5. Can scaling my boundary conditions improve the accuracy of my solutions?

In some cases, scaling the boundary conditions may lead to more accurate solutions. This is because scaling can help reduce the effects of numerical errors and improve the conditioning of the problem. However, it is not a guarantee and should be carefully evaluated in each specific case. It is also important to note that scaling may not always result in improved accuracy and could even lead to worse solutions if not done correctly.

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