Help needed to resolve a CFD differential equation
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Hi everyone,
I wondering if it's possible to resolve the following differential equation for 'k'? If so, could someone guide me through the process of resolving it? Thank you very much! Best Regards |
Maybe try with the following substitution:
so that: then apply the chain rule on the left hand side and see what happens. If you are lucky you will be left with something linear and integrable. EDIT: nope, b is a bitch and won't let you have a linear form in this case |
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Thank you very much for answering!
I was trying to make an attempt on trying to find for 'k' on the turbulent kinetic energy equation (k-epsilon) by using the turbulent viscosity equation (linear) instead of using the assumption that the productivity (Gk) is equal to the dissipation (epsilon). That why the last two term doesn't vanish and the equation become in this form. There is maybe an alternative by using the dissipation equation instead, but I think the equation become non-linear also. I ended up with the following equation, but I wasn't sure if it was correct. Even though, it's clearly non-linear and because of I wasn't sure how to integrate the equation. Again, thank you for your time and your help! |
Quote:
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Thank you very much for sharing this information! It obviously a good paper and I'll take look in depth what the author did.
What I was trying to attempt is to solve for 'k' in order to have another analytic profile. Not at the wall, but for the domain. I've seen in the literature that other 'k' profile has been obtain by assuming that the production is equal to the dissipation (https://www.sciencedirect.com/scienc...67610508001815). I found out by doing so that the turbulent viscosity is no longer linear. So, I want to keep the turbulent viscosity linear, and trying to find another 'k' profile by resolving the TKE equation and then, I end up with the differential equation in my first post. Thank for the discussion. |
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