# Exact solution of N-S eq. in Kim and Moin's paper

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 January 21, 2012, 07:45 Exact solution of N-S eq. in Kim and Moin's paper #1 New Member   Kyounghwa Kim Join Date: Jan 2012 Posts: 9 Rep Power: 7 Hello. I'm Kyounghwa. I'm going on check my New solver for N-S eq. I have a question. There are exact solution of N-S eq. about decaying vortices. u(x,y,t)=-cosx*siny*exp(-2t) v(x,y,t)=sinx*cosy*exp(-2t) p(x,y,t)=-1/4*(cos2x+cos2y)*exp(-4t) These equations are in Kim and Moin's paper. "Application of a Fractional-Step Method to Incompressible navier-Stokes Equations" in 1985. This eq. satisfies divergence free. But, I can't solve by just substituting into Incompressible N-S eq. because the boundary condition of exact solution changes for time(t). What will I do? Please, give me an idea. I don't know anything. I have one more question. How to obtain a exact solution with boundary conditions of u and v are zero? Last edited by Kyounghwa; January 21, 2012 at 08:04. Reason: It's mistake.

January 21, 2012, 08:08
#2
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Quote:
 Originally Posted by Kyounghwa Hello. I'm Kyounghwa. I'm going on check my New solver for N-S eq. I have a question. There are exact solution of N-S eq. about decaying vortices. u(x,y,t)=-cosx*siny*exp(-2t) v(x,y,t)=sinx*cosy*exp(-2t) p(x,y,t)=-1/4*(cos2x+cos2y)*exp(-4t) These equations are in Kim and Moin's paper. "Application of a Fractional-Step Method to Incompressible navier-Stokes Equations" in 1985. This eq. satisfies divergence free. But, I can't solve by just substituting into Incompressible N-S eq. because the boundary condition of exact solution changes for time(t). What will I do? Please, give me an idea. I don't know anything. I have one more question. How to obtain a exact solution with boundary conditions of u and v are zero?
This solution is periodic in x and y, just put periodic boundary conditions

January 21, 2012, 08:57
I don't understand.
#3
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Kyounghwa Kim
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Quote:
 Originally Posted by truffaldino This solution is periodic in x and y, just put periodic boundary conditions

I don't understand.

There is exp(-2t) in equation.
So, u and v change in time. Am I wrong?

January 21, 2012, 10:05
#4
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Kyounghwa Kim
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Quote:
 Originally Posted by truffaldino This solution is periodic in x and y, just put periodic boundary conditions
You mean...time is fixed?
Then, will I check for one clock?

January 21, 2012, 11:54
#5
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cfdnewbie
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Quote:
 Originally Posted by Kyounghwa You mean...time is fixed? Then, will I check for one clock?

no, time is notr fixed. What he meant is that the solution stays periodic in space, and decays in time. Just put periodic bcs on your spatial domain!

January 23, 2012, 10:36
OK~
#6
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Kyounghwa Kim
Join Date: Jan 2012
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Quote:
 Originally Posted by cfdnewbie no, time is notr fixed. What he meant is that the solution stays periodic in space, and decays in time. Just put periodic bcs on your spatial domain!

Ok. I'm understanding.
I will try to do. And I will report.
Thanks.

Last edited by Kyounghwa; January 23, 2012 at 10:37. Reason: Add something.

 Tags exact solution, kim and moin, navier stokes equation

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