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

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Old   January 21, 2012, 07:45
Post Exact solution of N-S eq. in Kim and Moin's paper
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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.
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Old   January 21, 2012, 08:08
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Quote:
Originally Posted by Kyounghwa View Post
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
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Old   January 21, 2012, 08:57
Default I don't understand.
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Kyounghwa Kim
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Quote:
Originally Posted by truffaldino View Post
This solution is periodic in x and y, just put periodic boundary conditions

I'm very sorry about that.
I don't understand.

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

Please, explain in greater detail.
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Old   January 21, 2012, 10:05
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Quote:
Originally Posted by truffaldino View Post
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?
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Old   January 21, 2012, 11:54
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Quote:
Originally Posted by Kyounghwa View Post
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!
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Old   January 23, 2012, 10:36
Default OK~
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Originally Posted by cfdnewbie View Post
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.
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