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Using integrals over variables in the model definition
Posted 06.05.2015, 16:31 GMT-4 Parameters, Variables, & Functions, Studies & Solvers Version 5.0 3 Replies
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We have a 2D model involving fluid flow and transport of diluted species. The latter includes an "R term," which adds a source for the species. We would like R to be a function of the spatial position, R(x',y'), computed as an integral over y and the species concentration itself. So, the integral involves both y' and a dependent variable: R(x', y') = integral from y0 to y' of F( tds.c(x',y) dy .
Questions:
1. Can COMSOL do this, or will it upset the minimization over the mesh?
2. How do we implement this? Some pieces of F(tds.c) are coded in variables right now. Do we use the "component coupling" approach shown in www.comsol.com/blogs/overview-integration-methods-space-time/ ? Or, do we use the additional physics interface approach from that link?
Does anyone know of a sample model that does something similar. As usual, I'm having trouble finding the right documentation section.
Just to emphasize- we're not looking to do integrals for post-processing. The integrals define the model and affect the solution.
Thanks.
Questions:
1. Can COMSOL do this, or will it upset the minimization over the mesh?
2. How do we implement this? Some pieces of F(tds.c) are coded in variables right now. Do we use the "component coupling" approach shown in www.comsol.com/blogs/overview-integration-methods-space-time/ ? Or, do we use the additional physics interface approach from that link?
Does anyone know of a sample model that does something similar. As usual, I'm having trouble finding the right documentation section.
Just to emphasize- we're not looking to do integrals for post-processing. The integrals define the model and affect the solution.
Thanks.
3 Replies Last Post 07.05.2015, 11:45 GMT-4
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Posted:
9 years ago
Hello Ed,
You can use the additional physics approach presented in the blog, except that your integration is relative to y not x and so your beta will be (0,1), not (1,0).
I am attaching a basic model that shows this. In it I set up the transport of diffuse species physics so that c has the analytical solution c(x,y)=y; this allows you to double-check that the solution is correct: u=.5*y^2.
Best,
Jeff
You can use the additional physics approach presented in the blog, except that your integration is relative to y not x and so your beta will be (0,1), not (1,0).
I am attaching a basic model that shows this. In it I set up the transport of diffuse species physics so that c has the analytical solution c(x,y)=y; this allows you to double-check that the solution is correct: u=.5*y^2.
Best,
Jeff
Attachments:
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Posted:
9 years ago
Thanks, Jeff. I'll explore the model you sent. Can you help me understand why the approach is to add additional physics vs. a coupling component? I was just about to try a projection coupling component. I'm asking so that I can deepen my understanding of COMSOL concepts.
Thanks,
-Ed
Thanks,
-Ed
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Posted:
9 years ago
Hi Ed,
It may well be possible to achieve the same results by other means, including component couplings, but the additional physics approach is intuitive to me and follows exactly what's presented in the blog (With the transposition of x and y, of course).
Best,
Jeff
It may well be possible to achieve the same results by other means, including component couplings, but the additional physics approach is intuitive to me and follows exactly what's presented in the blog (With the transposition of x and y, of course).
Best,
Jeff