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Function varying in time and space
Posted Nov 11, 2020, 12:10 p.m. EST Parameters, Variables, & Functions Version 5.5 6 Replies
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Hi everyone! I would need your help :) I am implementing a model using laminar flow physic in which I need to apply a boundary velocity perpendicular to the boundary itself that varies in both time and space. So, I would like this velocity on the boundary to activate after a certain time interval and move as an impulse along the boundary itself( something like a soliton)
I tried to multiply some functions but I couldn't solve it. Using a rect(t) I think I can solve the problem of 'activate' the velocity after a certain time but how can I set the movement along the boundary itself?
Does anyone have any suggestions? Thank you very much for your kind help Florinda
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Florinda,
in case the movement is intended along the x-axis with velocity v the boundary function would look like f = f(x(t)) = f(v*t). f may be the Gauss function as indicated in your animation.
With f = rect(t0)f(vt) you switch it at t = t0. You may need to smooth the rectangle function in order to get a time dependent solver to converge.
Cheers Edgar
-------------------Edgar J. Kaiser
emPhys Physical Technology
www.emphys.com
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Dear Edgar, thank you for your kind reply.
I tried to implement the function as you suggested but I didn't solve the problem of the impulse moving in space (along the x-direction).
As you can see in the attached gif, the function is activated after the time indicated by t0 but does not propagate along the x axis but starts from the whole boundary at the same time. I tried to indicate the units of measurement by setting velocity(m/s)t(s) within the function gp1(Gaussian impulse) in such a way as to underline the dependence on space rather than time but I was not able to solve the problem.
Thank you for your help
Florinda
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Dear Florinda,
Will using the following solve your issue: on the inlet, use the following expression: gp1(x-tB) Here the gp1(x) is your gaussian function, which should be setup in such a way that the location at t=0 is correct. The tB makes sure that the center is moving with time (t). B is the scaling for how fast it should move. Eg. at t = 1 s, the location is now at B.
best regards, Frank
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Dear Frank, thank you so much.
Do you think that I can set this condition to a leaking wall instead of an inlet? I need to implement a couette profile of the velocity field, so according to your geometry that is similar to mine I need to set these conditions: 1. boundary on the top: no slip; 2. boundary on the left inlet pressure=0; 3. boundary on the right outlet pressure=0; 4. boundary on the bottom: leaking wall, fluid velocity, on x this function
according to your suggestion I defined my gp1 (centered in 0) and I wrote as function 1e-3 gp1(x-t1e-3) my rectangle left corner on the bottom is in (0,0)
my boundaries are 3 mm and the velocity is 1 mm/s, but I cannot obtain your same result.
Thank you for your help Florinda
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Dear Florinda,
attached my file so you can see what I did. I hope that helps. Good luck with the model.
Best regards, Frank
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Dear Frank, thank you so much for your kind help! thank you Florinda