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

Kyounghwa · January 21, 2012, 07:45

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?

truffaldino · January 21, 2012, 08:08

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

Kyounghwa · January 21, 2012, 08:57

Quote:

Originally Posted by truffaldino

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.

Kyounghwa · January 21, 2012, 10:05

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?

cfdnewbie · January 21, 2012, 11:54

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!

Kyounghwa · January 23, 2012, 10:36

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.

January 21, 2012, 07:45	Exact solution of N-S eq. in Kim and Moin's paper	#1
Kyounghwa New Member Kyounghwa Kim Join Date: Jan 2012 Posts: 9 Rep Power: 14	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)=-cosxsinyexp(-2t) v(x,y,t)=sinxcosyexp(-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.