|Jul10-12, 05:20 PM||#1|
Problem: flux through prism faces
I need help regarding a practical problem I'm facing. It's not a homework/coursework, It's a real-life problem.
I have the values of a vector field (wind) given in six coordinates in 3D space. Those coordinates are the vertices of a triangular right prism (looks similar to my problem: http://i.imgur.com/2TU7D.png).
I would like to find the flux of this vector field through each lateral face of the prism. The components of the vector field may be approximated by linear functions.
My goal is to find the flux through the top face, given that the flux through the bottom face is null.
I'm trying to solve this numerically, i.e., using tools such as Matlab/Octave.
How could I do this?
Any suggestion (a reference for a method, a similar example, etc.) is welcome.
Sorry if this isn't the best place to post this kind of question, but since it's about flux I thought it would be included in General Physics section.
|Jul11-12, 01:48 AM||#2|
Is the wind moving in a curved path? Sounds like the maths would be horrible.
|Jul11-12, 05:29 AM||#3|
In fact, it's an application of divergence theorem; sorry for not mentioning this. That's why Petyab is right in suggest Gaussian surfaces.
I'm assuming that the volume integral of 3D wind divergence is null. Thus, the flux through the closed surface bounding the volume must be null. I know that the flux through bottom face is zero. Therefore, the flux through the top face must equals the total lateral flux.
Despite the relevance of those assumptions, my point is how to numerically find the fluxes considering I don't have a function for my vector field. Moreover, I have the vector field given only in specific points in space.
|flux, numerical methods, prism, vector field|
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