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Function varying in time and space

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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



6 Replies Last Post 17 nov. 2020, 15:43 UTC−5
Edgar J. Kaiser Certified Consultant

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Posted: 4 years ago 11 nov. 2020, 17:13 UTC−5
Updated: 4 years ago 11 nov. 2020, 17:24 UTC−5

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
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(v*t) 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

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Posted: 4 years ago 16 nov. 2020, 09:22 UTC−5

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

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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Posted: 4 years ago 16 nov. 2020, 10:47 UTC−5

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

Dear Florinda, Will using the following solve your issue: on the inlet, use the following expression: gp1(x-t*B) 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 t*B 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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Posted: 4 years ago 16 nov. 2020, 13:24 UTC−5
Updated: 4 years ago 16 nov. 2020, 13:25 UTC−5

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

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-t*1e-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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Posted: 4 years ago 17 nov. 2020, 03:14 UTC−5

Dear Florinda,

attached my file so you can see what I did. I hope that helps. Good luck with the model.

Best regards, Frank

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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Posted: 4 years ago 17 nov. 2020, 15:43 UTC−5

Dear Frank, thank you so much for your kind help! thank you Florinda

Dear Frank, thank you so much for your kind help! thank you Florinda

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